BHMS

Yes, you can get admission to a private college for a BHMS course in Maharashtra with 129 marks in NEET. The Bachelor of Homeopathic Medicine and Surgery BHMS degree programme focuses on homeopathic medical knowledge. It is a 5-year, 6-month long course. Which includes a 1-year internship. A list of the colleges in Maharashtra which provide BHMS courses is given below.
1-Lokmanya Homeopathic Medical College, Pune.
2-Bharati Vidyapeeth Homoeopathic Medical College, Pune.
3-Smt Chandaben Mohanbhai Patel Homoeopathic Medical College, Mumbai.
4-Dr GD political Foundations Y M T Homoeopathic Medical College Hospital, Navi Mumbai.
5-Dhondumama Sathe Homoeopathic Medical College, Pune. I hope this will help you.

According to the information you have provided, your All-India (AI) rank is approximately more than four Lacs.
Therefore, you can not get admission in Gujarat to a government college in the BHMS course. The cutoff for the BHMS medical course in most government colleges, like
1- The Government Homoeopathic Medical College, Patan, Gujarat, was ranked under 1,566,473 in 2021 for the Schedule Caste category.
2- Gujarat Homeopathic Medical College, Gujarat, was ranked under 1,82,213 in 2021 for the Schedule Caste category. This information is based on the previous year's results. For this year, results may be different because they can depend on many factors like domicile, gender, category, etc.

You did not provide proper information like category, domicile, etc., so it is difficult to predict accurately the college. According to your marks, your rank is more than 4.5 Lakh. You have fewer chances of getting admission into government colleges for the BHMS course. However, you can try getting admission into government colleges and private colleges that offer MBBS dental courses, nursing courses, etc. I'm suggesting some colleges according to your rank. A list of colleges is given below.
1- GITAM Institute of Medical Sciences & Research, Visakhapatnam.
2- Saveetha Dental College, Chennai.
3- Mahatma Gandhi Medical College and Research Institute.
4- MBBS-Bachelor of Medicine and Bachelor of Surgery.
5- Meenakshi Ammal Dental College and Hospital.
If you want more information regarding the college, course, or anything else, kindly visit the given link (https://www.shiksha.com/medicine-and-health-sciences/neet-college-predictor).
For this year, results may be different because they can depend on many factors like domicile, gender, category, etc. This information is based on the previous year's results.

Your All-India rank is estimated to be more than 2 lacs based on the details you have given. In Uttar Pradesh, the cutoff for the BHMS course was under 1.57 lakh rank in 2021 in most of the government colleges, like the State Homoeopathic Medical College and Hospital, Ghazipur.
You may have few chances with state quota to get a government seat in select colleges like the State Homoeopathic Medical College and Hospital, Gorakhpur, where the SC category closing rank was around 2.47 lacs.
Similarly, you may get a seat in select colleges like Swami Kalyandev Government Ayurved College, Muzaffarnagar, for the BAMS course if your rank is under 2.3 lacs.
Keep in mind that the actual cut-off for this year will vary depending on numerous factors like available seats and the number of applicants, while this estimate is based on the 2021 NEET UG cut-off.

MBBS Bachelor of Medicine and Bachelor of Surgery
BHMS Bachelor of Homeopathy Medicine and Surgery
BAMS Bachelor of Ayurvedic Medicine and Surgery
BUMS Bachelor of Unani Medicine and Surgery
BDS Bachelor of Dental Surgery
B Sc AH (Animal Husbandry) Bachelor of Veterinary Sciences
B Sc Bachelor of Science
B Sc Microbiology Bachelor of Science in Microbiology
B Sc Biotechnology Bachelor of Science in Biotechnology
B Sc Bio Chemistry Bachelor of Science in Bio Chemistry
B Sc Nursing
B PT Bachelor in Physio Therapy
B.Pharma Bachelor in Pharmacy
B Sc Agriculture Bachelor of Science in Agriculture
B Sc Horticulture Bachelor of Science in Horticulture
B Sc Environmental Science Bachelor of Science in Environmental Science
B F Sc Bachelor in Fisheries Sciences
B Sc MLT Bachelor in Medical Technology
B Sc Occupational Therapists
B Sc Audiology
B Sc Speech and Language Pathology
B Sc Radiography
B Sc Rehabilitation Therapy
B Sc Food Technology
B Sc Nutrition and Dietetics
B Sc Botany
B Sc Zoology
B Sc Anthropology
B Sc Home Science.