Hii....

As you that you scold 378 in NEET examination

 By scoring 360 out of 720 ,you you are qualified to attend counselling of colleges but with the score of 378  you are not main you are not able to get government colleges for MBBS and BDS but you may get private colleges for MBBS and BDS with your marks...

In order to avail the 85% state quota you need to get a score of above 500 possibly above 550 to get into a good MBBS Government College and score of above 400 to get into a good BDS college
For the 15% all India quota your rank ,definitely needs to be high enough and you need to score above 550 to avail the seats in the best medical colleges across India ...

But if you have reservation certificate... you can apply for reservation quota and  its may help you in getting admission and you can try even in government colleges..

Hope the best !!

All the best!!