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.

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.