The serial range and the "H" makes this gun sound like a Super Fox HE Grade chambered for 3" shells. They were made from 1923 to 1942. The first one was serial# 28069. It was made for John Olin, owner if Western Cartridge Company and future owner of Winchester Arms Company. He developed the Super X 3" Shell.

What are the other markings stamped on the barrel flats and the frame?

Looks like what you have been given is a hell of a good Christmas bonus!

Ole Cowboy