The generator matrix

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

generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+104x^56+792x^57+2400x^58+4380x^59+7663x^60+10236x^61+14435x^62+16408x^63+18056x^64+17144x^65+14544x^66+10086x^67+7331x^68+4006x^69+2043x^70+750x^71+408x^72+156x^73+82x^74+38x^75+4x^76+2x^77+2x^79+1x^80

The gray image is a linear code over GF(2) with n=512, k=17 and d=224.
This code was found by Heurico 1.16 in 138 seconds.