Does it matter what gauge power cord that you use?

No, there is no technical reason why a heavier gauge power cord would provide any benefit whatsoever.

While there may be no technical reason a larger guage cord will work better, my experience is that the larger guage cords that I have tried have been better performers overall with my integrated amplifier. I have not tried anything heavier than 10 guage but I think that a heavier cord may have advantages over a smaller one with a fairly current hungry piece of equipment. With my digital gear, I have not found that guage is as significant, and actually use a 26 guage DIY cord on my DVD player that sounds better than a Cardas Golden cord which I had used on that piece before. I wouldn't consider, however, even putting that cord on my amp for obvious reasons.

I have replaced all of my stock powercords with DIY cords via Chris VenHaus recipes. I did the first one because the dollar investment was minimal and if it didn't work that well I would not be out very much. I replaced all of the cords because the sonic differences were not subtle, but huge.

It is possible to buy astronomically expensive cords, which I have never done so I cannot address the value of them, but great improvements can be had for under $100 if you don't mind doing a little work.

I don't know if just adding heavier gauge cable will do much for you, you need the right cable. I used Beldon 83802 for all of my cables.

Try a better cord, you won't go back to stock cords again!