Are you trying to find the exact model, or simply add a heavy-barreled semi-auto 22 to your collection? If you're trying to find the same one.. I think we'd need a little more info to help narrow that down. If it's a modern(ish) factory gun you want...there are a few I could recommend, but knowing your budget would be key there.
As for what they're called~heavy-barreled 22s are sometimes called "HB"...."Target"...."Varmint" models, depending on the manufacturers. Some manufactures just kind of use chunky barrels (ie. Marlin 795) but don't give them any special designation/name. In fact, a "heavier" barreled version of the 795 was even made for a while called the Marlin 7000. A gun I'm on the lookout for simply because I like the look of it. My 795s (x2) are both very accurate guns for what they are.