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

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+228x^59+223x^60+384x^61+427x^62+614x^63+592x^64+546x^65+318x^66+276x^67+147x^68+148x^69+67x^70+94x^71+11x^72+10x^73+1x^74+4x^75+2x^76+2x^78+1x^98

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 1 seconds.