The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+183x^58+228x^59+436x^60+418x^61+623x^62+578x^63+529x^64+364x^65+278x^66+144x^67+164x^68+18x^69+65x^70+42x^71+18x^72+2x^74+4x^76+1x^98

The gray image is a code over GF(2) with n=504, k=12 and d=232.
This code was found by Heurico 1.16 in 0.484 seconds.