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

generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+67x^58+4x^59+118x^60+52x^61+271x^62+328x^63+434x^64+328x^65+238x^66+52x^67+55x^68+4x^69+45x^70+24x^72+18x^74+7x^76+1x^82+1x^104

The gray image is a linear code over GF(2) with n=512, k=11 and d=232.
This code was found by Heurico 1.16 in 0.329 seconds.