With rank 3166, you do have chance to get government MBBS college

But please consider the fact that cutoff has been increasing every year depending upon number of seats available, number of candidates and exam difficulty.

Some of the government MBBS college in Maharashtra are-

• BKL Walawalkar Rural Medical College, Ratnagiri
• Ashwini Rural Medical College Hospital and Research Centre, Solapur)
• Dr Shankarrao Chavan Government Medical College, Nanded
• Byramjee Jeejeebhoy  Medical College, Pune
• Dr Panjabrao Deshmukh Memorial Medical College, Amravati )
• Dr Ulhas Patil Medical College and General Hospital, Jalgaon
• Dr Panjabrao Deshmukh Memorial Medical College, Amravati
• Government Medical College and Hospital, Jalgaon
• BKL Walawalkar Rural Medical College, Ratnagiri

https://medicine.careers360.com/neet-college-predictor?utm_source=qna&utm_medium=neet_cp

Best of luck