While waiting off I went and purchased a Slimport adapter (see pictures below) at Verkkokauppa.com outlet for 12 €. At the moment it's possible to mirror the screen of my phone and use TV as a second monitor. What did I do? I attached a HDMI cable to my TV. Next Slimport adapter to HDMI cable and lastly Nexus 4 to Slimport adapters micro USB port. Suddenly the screen of my phone showed up on TV. There was no need to change any settings in Android.
Why is Maru OS so important and interesting project? Because of Microsoft. They have their Continuum going on. It's possible to turn Windows phone into PC. With help from Maru OS assorted Android phones will be able to do the same.
In case you got interested, please read through how to flash your phone. All the information you have will be wiped. Remember you are doing it at your own risk.
Slimport adapter ends
Slimport adapter has an extra port for power,
however I didn't need it