The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1 2X+2  2  2  1  1 3X X+2  1  1 3X+2  1  0 X+2 3X+2  1  1  1  1  X X+2  1  0  1  1  1  1  1  1  1 2X  1  X  1  1  1  1  1  1  1 3X  1  1 2X  1  1  1 3X+2  2  1  1  1  1  1
 0  1  0 2X 2X+3  3  1  X 3X+3 3X X+3  1  X  1 X+3 2X+2  1  0  X X+1  1 2X+1  1  1 X+2  0 3X+3 3X 2X+2  1 3X  1  1 3X+1 2X+1  2 2X 2X+2 3X+3 X+1 X+2 X+2  1 2X+1  2 2X+3 2X X+1  3 3X+2 2X+2 3X+2 X+2  1 2X+3  1  1  2  2  X 3X 3X+1 3X+3  0
 0  0  1 3X+1 X+1 2X 3X+1 3X  1 2X+1  X  X  1 3X+3 2X  3 3X  1 2X+2 X+1  0 3X+2 2X+3 X+3  1 X+2 X+1 3X+3 X+3 2X+1  1 3X+3  2  2 2X+1  0  3  X  3 3X  1 2X+3 3X+2  X 3X+1  2  1 3X+3  3 X+1  1  1 X+2 3X 3X+2 2X+3 3X+1  1  1  0 3X+2 3X+2 3X  0

generates a code of length 64 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+122x^60+616x^61+560x^62+804x^63+550x^64+448x^65+269x^66+264x^67+145x^68+136x^69+57x^70+84x^71+21x^72+16x^73+1x^74+1x^76+1x^86

The gray image is a code over GF(2) with n=512, k=12 and d=240.
This code was found by Heurico 1.16 in 0.25 seconds.