Still having a 386 system, come on - it is too old. My personal advice would be to get rid of it. I feel sorry to say that, but it is far far away from todays powerful machines. I think that processor/mother board was designed for DOS and the modern day OS won't work on it. It will be just waste of time trying to get ubuntu to work on it.
Try and see if any of the FreeBSD or OpenBSD works on it, but i doubt that too. Sorry.

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