Hello Aspirant,

Any rank between 1 to 20k is considered to be a very good rank in a state-level engineering entrance examination like KCET. So you got the rank 14k which is pretty good for taking a admission in top Engineering colleges.

Considering  the score you mentioned, It is difficult to predict your college based only on rank because there will be reservation in KCET seat allotment.   Since you are from GM category there will be tough fight to get seat in these top colleges but don't lose hope try for all the 3 rounds you will get one of these top college. If you have Kannada or Rural or some other reservation then it will be easier to get a seat.

Some top engineering college list :

1. R.V. College of Engineering
2. BMS Institute of Technology
3. KLE Institute of Technology known as BVB Hubli
4. M.S. Ramaiah Institute of Technology
5. PES University Bengaluru
6. NMAM  Institute of Technology , Karkala
7. SDM College of Engineering, Dharawad.
8. NIE Mysore
9. JSS Mysore
10. Bengaluru Institute of Technology
11. Dayanand Sagara Institute of Technology
12. Nitte Meenakshi Institute of Technology

you can use college predictor link from the given link :-

All the best...!