Try entering "linux on 32mb ram" into google. You will get a lot of discussion threads for suggestions. It has been a while since I have done it, but I have run Ubuntu and before that Red Hat on some really old hardware that dates back to the late 1990s; back when 16 to 32 mb of ram was still common. Lastly, I ran a copy of Ubuntu server 9.04 edition (no X) on that machine before retiring the machine after a failure of the add on SATA card. It served as my email, dhcp, and dns server for over a year before that.
I personally take "minimum system requirements" with a good dose of salt, having lived through the days of a higher clock speed Pentium 2 and software that forced you to upgrade just because it could, but running current versions of Ubuntu may be a bit much as they tend to be resource hogs.