I wouldn't. I don't think it's practical to even try to install Ubuntu within 128MB.
Ubuntu is compiled to be useful, not frugal with disk space. A prime example of this is: each of Ubuntu's kernel packages is about 150MB. It's designed to be flexible, not small.
Yes, you could roll your own for just your hardware (make localmodconfig
) but you'll likely end up needing to roll a lot more too. A customised start-up process, strip out Upstart/Systemd, streamline the Xorg drivers.
Your biggest problem, perhaps, is installing. Assuming you can get the final payload beneath 128MB, the only way I can think to get it on the end device is to do a raw copy onto its media (essentially, flashing it from a virtual install you've done and trimmed elsewhere).
And it's not just the up-front time needed, you also have to consider maintenance. The more you customise, the less can be updated automatically. Keeping on top of security issues will be harder because you won't have somebody compiling and packaging things for you.
So yes, you could spend a lot of time doing this just to get Ubuntu and the useful things Ubuntu brings with it. Or you could use something that is designed to be used on an ancient computer. I know which I'd pick.