360 4-speed manual transmission?

I have always been wondering if there was ever a 360 engine paired with a 4-speed manual transmission that made out of the factory? I always hear about the 318 4-speeds and the 340 4-speeds, but never any 360 4-speeds. As I said, I'm not sure if there were ever made out of the factory like that, but that's why I'm asking you guys. Also if there was not, would it be possible to put a 340 4-speed transmission setup on a 360 engine? I know you would have to change the flywheel, but I'd thought I would ask still. Any answers are appreciated, I'm just curious. Thanks!