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  X  1  1  0  1  1  1  1  X  1  1  1  1  1  1  1  1 X^3  1  X  1 X^3+X^2  1  1 X^3  1  X X^2  1  1  X  1 X^2  1  1  1  X  X X^2  1  1  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X  0 X^2+X X^3 X^2+X X^3+X X^2 X^2  X  0 X^2+X X^2 X^3+X  0  0 X^3+X^2+X X^3+X X^3+X  X X^3+X X^3+X^2 X^3+X^2 X^3+X X^2+X  X X^3+X^2 X^3+X^2  X X^3+X X^3 X^3+X X^3+X^2+X  X X^2+X X^3+X X^2+X  X X^2 X^3+X^2+X  X  X X^3+X^2+X X^2 X^3+X^2+X X^2  X X^2+X  X X^2+X X^3+X^2+X X^2+X X^3+X^2  X  X  0 X^2  0
 0  0 X^3+X^2  0 X^2  0 X^3  0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^3  0 X^2 X^2 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3 X^3  0 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0 X^3 X^3+X^2  0 X^3 X^2 X^2  0 X^3 X^2 X^2  0 X^2 X^2 X^2 X^3 X^3  0  0  0 X^3 X^3+X^2  0
 0  0  0 X^3+X^2  0 X^3 X^3 X^2 X^2 X^2 X^2  0  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3  0 X^2 X^3 X^2 X^3+X^2  0  0 X^3  0 X^2 X^2 X^2  0 X^3+X^2 X^3 X^3 X^2 X^2  0 X^3 X^3 X^2  0 X^3+X^2  0 X^2 X^2 X^2 X^3 X^3 X^2 X^3+X^2  0 X^2  0  0 X^3+X^2  0 X^3  0 X^3+X^2 X^3
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0  0  0  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3  0 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+72x^58+168x^59+180x^60+404x^61+368x^62+684x^63+418x^64+768x^65+260x^66+408x^67+125x^68+76x^69+52x^70+52x^71+34x^72+12x^74+4x^76+4x^78+3x^80+2x^84+1x^100

The gray image is a linear code over GF(2) with n=512, k=12 and d=232.
This code was found by Heurico 1.16 in 0.641 seconds.