As a kid... 19ish? I was pulled over on a deserted (2 in the morning) highway doing 150 in a 55 (see, I'd just had an Olds Rocket put in my 1980 Pontiac Grand Prix, so I had an excuse... other than just being stupid). Same situation as you (first time offender). Hired a lawyer. Plead guilty. Since I was a first time offender, in CT you can apply for accelerated rehabilitation (AR). Which means, you get off scott free, as long as you're able to go another 6 months with no traffic blemishes. At all. If you do, then the full penalty of the original and second offense applies.
Call a traffic lawyer, ask them about AR. Don't go into court looking like a scrub. Good attire and show respect. I suspect you learned your lesson. I know I did. To this day, never again. Good luck.