This Brix box from Gigabyte with Intel Core i5 comes with Intel Hd5500 integrated graphics and runs well with Ubuntu 14.04 and Mate 16.04.
For Installation on the SSD I used the rufus tool which allowed to prepare an EFI formatted USB stick.
The integrated graphics is good enough for media playback and light gaming in Ubuntu (steam works).
Don’t expect high frame rates with newer games.
Rufus project