I can play HD video files (1080) with mkv and mp4 extension by using XBMC Media Center on Ubuntu 14.04 x64 but I have my own computer that differs with yours. And even I can watch those file which are for 5.1 speakers with DOLBY quality by that software. But I am not sure about you and your computer. Maybe you can use it. Try it and after installation, update and upgrade your ubuntu.
You can install XBMC from Ubuntu software center that I did. But I suggest you can go on this link and pay attention to some tips there . And then run these commands:
sudo apt-get update
sudo apt-get upgrade
Some people have problems with XBMC on Ubuntu 14.04 X64. But I haven't had any after installing it and updating and upgrading Ubuntu 14.04. I don't know why but first I had a problem with XBMC. Nevertheless, after some days when my Ubuntu became up-to-date the problem was solved. And no error has been detected since that time. Besides I haven't had any problem with XBMC since that time. I think that all optional-add-ons with XMBC in Ubuntu software center must be selected first that I did. Then try to install XBMC.
I hope my solution will work for you too.