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  2  1  1  1  0  1  2  X  X  1  X  1  X  1  1  1  1  1 X^2  1  1  1
 0  X  0  X  0  2 X+2  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X+2  0 X^2 X+2 X^2+X  X  X X^2 X^2+2  X  X X^2+X X^2+X X^2+2  2 X^2+X  0 X^2+X+2 X^2+2 X^2+X+2 X^2+2 X+2  0 X^2+X+2 X^2  0  X  X X+2  2  0  0 X^2 X+2  2  X  0  2 X^2+X+2 X+2  X X^2+X  X X+2 X^2 X^2 X^2+2 X^2
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2 X^2+X+2  X  0  2 X^2+X+2 X+2 X^2  0  X X^2+X+2  2 X^2  X X^2+X+2 X^2 X+2  2 X^2  X  2 X^2+X+2  X X+2 X^2+2 X^2+X  2  0 X^2+X+2 X^2 X^2+X+2 X+2 X^2 X+2  0 X^2+2  0  X  0  X  0 X^2+X+2 X^2+X X^2+X X+2 X^2 X^2+X+2 X^2 X^2+X+2  2  X  X X^2+X X^2  X
 0  0  0  2  0  0  2  0  2  0  2  2  2  2  0  2  0  0  0  0  2  2  0  2  2  2  0  0  0  2  2  2  2  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  0  2  0  2  0  2  0  0  0  0  2  0
 0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  2  0  2  0  0  0  2  0  0  0  2  2  0  0  2  0  0  2  0  2  2  0  2  2  2  2  0  0  2  0  0  2  2  0  0  0  2  2

generates a code of length 63 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+248x^58+24x^59+549x^60+320x^61+730x^62+592x^63+626x^64+320x^65+348x^66+24x^67+179x^68+74x^70+52x^72+8x^74+1x^104

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 0.516 seconds.