The generator matrix

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

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+176x^59+341x^60+248x^61+586x^62+392x^63+795x^64+272x^65+528x^66+288x^67+240x^68+120x^69+36x^70+40x^71+18x^72+10x^76+2x^78+2x^88+1x^92

The gray image is a code over GF(2) with n=512, k=12 and d=236.
This code was found by Heurico 1.16 in 79.7 seconds.