If you don't have a non-resident permit, it is probably illegal to take the gun into MA. I'm looking at Chapter 140, section 131G, and it exempts for competition, and for meeting or exhibition of an organized group of collectors or hunting. It says nothing about going to the range. Even if you met those requirements, you would need a CT permit to carry. And that's just to POSSESS the gun in MA, no matter how you packed it.
BTW, the federal law doesn't help, either, since MA is your destination.
The only protection you have is the 2nd amendment to the U. S. Constitution, and that is mostly not in force these days.