I checked all solutions up tot S=1,500,000. Did not find another 3 x 3 magic square of 7 or more distinct squared integers. I did however find many with 6. They seem to get more rare the higher you get. The last one I found was:

532^2/980^2/476^2
433552/700^2/546448
868^2/140^2/696976

S = 1,470,000