Arduino, lcd 16x2 and UTP cable shows gibberish text?
Is the cable shielded? 
Have to performed continuity test on all leads of the cable to ensure there no break internally that could be causing an issue, or a short?

What is the impedance of your total length of cable?

These sorts of checks will help you further narrow down the issue. If you are certain your wiring is correct, then the most probable issue is either a hardware failure (continuity test)
a hardware limitation (Too much resistance for accurate data travel)
Improper Hardware, unshielded wires can be subject to crosstalk, or signal corruption/distortion due to external signals interfering.