Today I got an answer by Gigabyte, not quite the answer I had hoped for: 

Dear  Erik ,
AMD Radeon R9 390 only can reach 4K@30Hz due to HDMI version 1.4a.
Only HDMI 2.0 can reach 4K@60HZ via HDMI port. On the other hand, the display devices should be support HDMI 2.0 as well.

I emailed them back:
Dear GIGABYTE-Team,
Perhaps I was unclear in my formulation, but I am quite sure you missed my point unfortunately. I will retry:

I was and am aware of the technicical limitations of HDMI 1.4a which is located on my R390 card (this is 4k 30Hz). So far so good.
I am also aware HDMI 2.0 is needed for 4k 60Hz.

This is exactly the reason I bought a CLUB3D CAC-1070 adapter (please familiarise yourself with this adapter before continuing: http://www.club-3d.com/index.php/products/reader.en/product/displayport-12-to-hdmi-20-uhd-active-adapter.html).

It converts the Displayport 1.2 output to a HDMI 2.0 output.

My device chain setup is as follows:
Computer>Gigabyte AMD R390 > displayport 1.2 > CAC-1070 > HDMI 2.0 > HDMI 2.0 cable > HDMI 2.0 input on UHD TV Samsung JU6650.

Superfluously, I have not connected to the HDMI1.4a port, but to the Displayport.

Within this device chain I have exchanged all devices in order to isolate the problem:

• I downgraded to 8bit color depth
• I have tried a different HDMI 2.0 cables
• Then I tried different drivers (catalyst to crimson 16.5.1)
• I tested with all configurations on my Monitor (UHD Color ON, source input etc)
• I reïnstalled windows
• I updated the firmware of Motherboard
• I updated the firmware of GPU
•  I brought the CAC-1070 adapter and my cables to a store where I tested with an identical SamsungJU6650 Monitor and a gaming laptop with displayport 1.2 (this was succesful and rules out the problem is in the cable or CAC-1070 adapter)
• I brought over a friend’s computer with a R290. I connected his PC to my TV via Displayport 1.2 > CAC 1070 > HDMI 2.0 > Cable > Samsung and it worked at 4k60Hz. Note: this confirms that my display device support HDMI 2.0 as you mentioned.
• Next, I placed his R290 in my computer/motherboard. I attached the CAC-1070 to the displayport 1.2 of the R290 and the adapter’s HDMI 2.0 output provided 4k60Hz. This rules out that the rest of my setup or OS is the problem.
• Next I placed my Gigabyte’s R390 in his system and connected the screen in the same way (DP1.2>CAC-1070>HDMI2.0>Cable>Samsung. This did not work.

This leads me to the conclusion it cannot be another device than the Gigabyte R390.

• I have seen my television work,
• I have seen my cable work,
• I have seen the CAC-1070 adapter work
• … R390
• I have seen my system work (be it with an other GPU). 
• The only time it does not work is in combination with the Gigabyte R390.

Please advice on how to proceed or what support I can count on from Gigabyte. Can you recreate/recognise the problem? If so can you provide firmware update if it is software related or exchange my GPU for an identical one to rule out hardware related issues?

I hope I have more clearly described the issue at hand.
I am looking forward to a workable answer.

Regards,

Erik Guldenaar

ps. please attend to the thread on the CLUB3d forum where I have posted pictures of the tests I described here.