
Quoting
flyingron
Your being "very sure" doesn't mean the officer didn't observe you failing to make a complete cessation of motion BEFORE the stop line/crosswalk/intersection.
Nothing you say is likely going to be compelling in light of the officer's expert testimony that you broke the law. Massachusets doesn't have a formal "take traffic school to get out of the ticket" option. Feel free to go to court, expect to lose unless something amazing happens.
You will get TWO POINTS on your NJ license for the out of state conviction. Your insurance company will hear about it. Whether they raise their rates is up to them (NJ doesn't have any mandatory scoring on these things). You may be able to offset the rate increase by taking a defensive driving course. Again, you'll have to ask your insurer.