HDMI 1.4 of any form, does not support 120hz in 2D. It is a common misunderstanding of the spec. Here is what is said:
http://en.wikipedia.org/wiki/HDMI
HDMI 1.4b was released on October 11, 2011.[138] One of the new features is that it adds support to 3D 1080p video at 120 Hz – allowing frame packing 3D format at 1080p60 per Eye (120 Hz total).[139] All future versions of the HDMI specification will be made by the HDMI Forum that was created on October 25, 2011.[37][140]
What that means, is in 3D using frame packing, HDMI 1.4b can support 120hz. It does this because it can send the left and right eye image in 1 frame. It actually sends the info at 60hz, but splits the 2 images up, and displays them in order at 120hz. This does not work in 2D.
You will require HDMI 2.0 for 120hz, which does not exist on current GPU's, so it can't be done on HDMI....With one kind of exception. Nvidia has started allowing 120hz over HDMI 1.4 on its cards by using compression. The quality is reduced, but it does allow HDMI to operate at 120hz.
Just get a new dual link DVI-D cable or use displayport.