The "76" (although it looks to be in a strange place in your string of proofmarks) likely is the chamber length, and that would be 3". I would not use Hevi-Shot in that gun. If you are waterfowling with it, or are in a nontoxic only area for upland birds, I'd recommend Kent's Tungsten Matrix. Great stuff.

If you're just looking for more range and don't need to use nontox, you might try the 2 3/4" 20ga magnums, 1 1/8 oz shot, usually buffered. They'll give you a pretty good kick in a Bernie Gamecock, but the buffering and the heavier shot charge will give you a denser pattern and a bit more range.