I want to run a Linux distribution in 256 color.
Doesn't matter which distribution can do it.
I tested Ubuntu 14.04, but it can't run lower than 16 bit. (using /etc/X11/xorg.conf)
Which distribution is better for me, and how can I configure that?
It sounds as if you want pseudocolor, which isn't well supported anymore. A thread on Xorg a few years ago pointed out a problem with the feature, but concluded by suggesting that it could work with a vesa driver. Alternatively, a discussion on a Raspberry Pi forum suggested using
Xephyr (a nested X server) in which one could run a client.
This guide describes launching wine in 256 color mode, but approach works for any other application as well. The solution is to create new X11 display (one way or another) with desired capabilities and to run application within it. I tested VNC-way and it worked like a charm.