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

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+57x^58+124x^60+24x^61+205x^62+360x^63+540x^64+360x^65+191x^66+24x^67+83x^68+52x^70+17x^72+6x^74+2x^76+1x^78+1x^116

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 0.328 seconds.