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

generates a code of length 64 over Z2[X]/(X^4) 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 linear code over GF(2) with n=512, k=12 and d=236.
This code was found by Heurico 1.16 in 1 seconds.