Hello, Phil:
I'm afraid you're out of luck. Your ASUS features an HDMI and a USB 3.1 Type-C port but no Display Port. The Intel Core i7-6770HQ CPU transfers graphics output via eDP, DP, HDMI or DVI. This means your CPU supports 4K, but it depends on the type of ports available on your ASUS.
An HDMI 1.4 port will transfer a max resolution of 4096 @ 24Hz. If your ASUS is fitted with HDMI 2.0 you might achieve 30Hz (my guess is it isn't). For true 4K @ 60Hz you'll need an actual display port - forget about adapters.
I'm not a USB expert and from what I've read the most recent developments with Type-C could conceivably transfer 4K @ 60Hz, in addition to all the other functions (e.g. hyper-speed data transfer and power charging). So you could try with a Type-C cable, but I doubt it'll work on your ASUS.
It all comes down to Intel's CPUs - and they typically 'max out' with DP, and the type of ports the manufacturer decides to fit into your machine - HDMI is still very much the trusted workhorse of graphics transfer.
Sorry,
GreyCatz.