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

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+119x^58+8x^59+162x^60+176x^61+376x^62+400x^63+388x^64+176x^65+115x^66+8x^67+81x^68+18x^70+4x^72+12x^74+3x^76+1x^112

The gray image is a code over GF(2) with n=504, k=11 and d=232.
This code was found by Heurico 1.16 in 125 seconds.