We’ve been able to run Ubuntu on Intel Atom Z3735F mini PCs, as well as other Linux distributions, for a while, but with an important caveat: HDMI audio would not work, so instead you had to use an external USB sound card to get any audio. Luckily the problem seems solved, as Linuxium has now released a script (audio-wifi-minix-neo-z64-release.sh) and relevant files that will patch your system to enable HDMI audio, and WiFI on MINIX NEO Z64W running Ubuntu.
Ian Morrison (Liuxium) compiled a Linux kernel and the Wi-Fi driver, together with a modified DSDT (Differentiated System Description Table) table to fix an ACPI bug. He used John Pemberton’s Bay Trail Audio HDMI patch, as well as help from Paul Kendall for identifying the ACPI DSDT table bug, Bastien Nocera (hadess) for the wifi source code and DroidMote Server / Client for the wifi pointer. A quick demo shows WiFi and HDMI audio working in Ubuntu.
It works on MINIX NEO Z64W, but I don’t see why it could not easily be adapted to any other Intel Atom Z3700 platform, you’d just need to patch the Linux kernel (3.16) and re-built it.