Hello dear, With this rank, you have high chances of the following colleges :-

1) Bhagalpur College of Engineering, Bhagalpur
2) Bhaktiyarpur College of Engineering, Patna
3) Gaya College of Engineering, Gaya
4) Nalanda College of Engineering, Chandi
5) Darbhanga College of Engineering, Darbhanga
Please visit the following link and fill the details to know more colleges for you :-
https://engineering.careers360.com/bcece-college-predictor

The official date for counselling has not yet been announced. However, it is expected that it will start in the last week of July.