Is it normal? I changed the tires before going on a trip and 20 miles in the light came on. I turned he car off and then on and light disappeared but came on again after 15-20 miles.
I have 2010 GT

 

does the 2010 GT have a 2WD mode? if not, then you either need to shave the new tires to be the same size as the front wheels...or purchase new tires for your front. in an AWD vehicle, all tires need to be the same. If you have 2WD mode, then you need to put new tires up front and wear them down until all tires are the same size.

I recently had to do this. running around in 2WD sucks.

 

It has "tarmac" which is I'm assuming 2WD mode.
Shame, the front tires have plenty of meat left, gonna buy 2nd set.

 

Tarmac is not 2WD, GT does not have 2WD mode.

 

Even though Tarmac feels like 2WD, it isn't. It is more front biased than the other modes.
I can't find it now but default for Tarmac is 90/10 to 70/30 or something like that.