The generator matrix

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

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+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 linear code over GF(2) with n=512, k=12 and d=236.
This code was found by Heurico 1.16 in 79.2 seconds.