I had tried to get some version of Linux running on my 386SX / 25MHz / 8MB RAM but only succeeded in getting BasicLinux[1] running bootstrapped from a DOS boot first. Somehow I had never found ELKS! But I was just able to trivially make a floppy and boot the system[2]. Amazing. Looking forward to playing with this.
I've been able to cross-compile from Linux (in Docker on my Mac; things didn't work well on macOS) to make binaries that run on the 386 under ELKS. Just had to juggle a few stock games to grab a couple dozen KB on the floppy to make room.
Also, check delicate linux:
http://delicate-linux.net/
Do not try X under Delicate Linux, it will run dog slow with 8MB of RAM.
If you can upgrade it to 16MB and some 486, X would be fine, with icewm set to a light plain theme, no desktop icons.