Hello, 

The last year's cut off marks for Karnataka State counselling under Open Category was 360 and above.

Following are some colleges in which you can try for admission through state quota.

1. Karwar Institute of Medical Sciences.

2. Chamarajanagar institute of Medical Sciences

3. Kodagu institute of Medical Sciences.

You can try for admission in MBBS in these colleges.. 

With a score of 377 you have good chances of admission in BDS courses in Karnataka.

Good Luck.