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  X  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 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^2 X^3+X^2 X^2  0 X^3  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^3 X^3  0  0 X^3+X^2 X^3+X^2  0 X^2 X^3 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0  0  0  0  0 X^3+X^2 X^2 X^3  0 X^3  0
 0  0 X^3  0  0  0  0  0 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 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 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0
 0  0  0  0 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3
 0  0  0  0  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0  0  0  0  0  0  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+39x^58+24x^59+40x^60+88x^61+300x^62+72x^63+1071x^64+8x^65+280x^66+8x^67+20x^68+24x^69+12x^70+8x^71+8x^72+8x^73+8x^74+16x^75+12x^76+1x^122

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 0.343 seconds.