Like others have said: Minix and others did. I ran Minix for a while when I had a 386sx (wish was like a 16 bit 386). In particular it lacked the protected mode that Linux used heavily.

So full 386 software didn't run on that. Minix was super fast but there was little you could do with it, sadly.

Of course pretty much all Intel computers still run Minix today as part of Intel's management engine.