The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 2a^2+2  1  1  1  1  1  1  1  1  1  1  1  1 2a^2+2a  1  1  1  1  1  1 2a^2+2a+2  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1 2a^2+2  1 2a+2  1  1  1  1  1  1  1
 0  1  0  1  a a^2 3a+3 a^2+3a a^2+3a+3 a^2+2a+1 2a^2+2 2a^2+3 a+2 a^2+2  1 3a^2+3a+1  2 2a^2+2a+3 a+3 3a^2+2 3a^2+3a 3a^2+3 2a^2+a+2 2a^2+3a+1 a^2+3 3a^2+3a+2 3a^2+3a+3  1 2a+3 a^2+2a+2 2a 2a^2+3a 3a+1 a^2+3a+2  1 2a^2+2a+1 a+1 a^2+a+3 a^2+3a+3 2a^2+1 3a+2  a 3a^2+2a+2 3a^2+3a+1  1 3a+2 a^2+2 2a^2+a+3 3a+3 a^2+3a+1  1 a^2+a+2  1 3a^2+a a^2+3a a^2+3a+1 3a^2+2a 3a^2+2a+1 2a+1 a+1
 0  0  1 a^2+2a+1  a 3a^2+3a+2  1 a^2+3a+3 2a^2+3a+1 a^2  3 a^2+a+3 2a^2+2 3a^2+2 a^2+2a+3 2a^2+2a+1 a+3 2a^2+a 3a^2+2a+1 2a 3a^2+3 a^2+3a+1 3a^2+a+2 3a a+1 a^2+3a+2 3a^2 2a^2+3a 2a^2+3 a^2+1 3a+2 a^2+2a 3a^2+3a+1 3a+1 3a^2+2a+1 a^2+a+3 2a+3 2a^2+2a+1  2 a^2+2a+3 2a 2a^2+3a+2 a^2+2 3a+3 2a+2 3a^2+2a+1 2a^2+3a 2a^2 2a^2+a+3 a^2 a^2+a+3  a a^2+2 2a^2+2a 3a^2+1 a^2+3a+1 3a^2+a+2 a^2+3a a^2+3a 3a^2

generates a code of length 60 over GR(64,4) who´s minimum homogenous weight is 404.

Homogenous weight enumerator: w(x)=1x^0+7952x^404+8400x^405+3192x^408+3360x^409+27160x^412+22512x^413+10304x^416+6720x^417+36512x^420+34608x^421+19152x^424+11424x^425+43064x^428+27664x^429+42x^440+63x^448+14x^472

The gray image is a code over GF(8) with n=480, k=6 and d=404.
This code was found by Heurico 1.16 in 21.7 seconds.