The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3  1  1 X^2  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1  1  0 X^2+X  1  1  1  1  1 X^3 X^3+X^2+X  1  1  1 X^3  1  X  1  1  1 X^2 X^3+X  X  X X^3  1  1  1  X  1  1  1  1  1  1  0  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X  1  1 X^3 X+1 X^3+X^2+X  1 X^3+X^2+X+1 X^2  1  X  1 X+1 X^3+X^2+X+1 X^2+1 X^3+1 X^2+1  0  1  1 X^3+X^2+X X^3+X+1 X^3+X^2+1 X^2 X^2+X  1  1 X^3+X^2+1 X^3+1 X^2  1 X^3+X+1  1 X^2 X^2+X X^3+X  1  1  0 X^3+X  X X^3+X^2+X X^3+X X^3 X^2+X  X  X X^3+X X+1 X^3+X^2+X+1 X^3+X^2+X+1  1 X^2+1 X^3
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0 X^2 X^3 X^2 X^3 X^2 X^2  0 X^3  0 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^2 X^3+X^2
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0  0 X^3
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 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 59.

Homogenous weight enumerator: w(x)=1x^0+68x^59+288x^60+450x^61+524x^62+494x^63+606x^64+468x^65+490x^66+304x^67+202x^68+100x^69+53x^70+24x^71+4x^73+2x^74+4x^75+6x^76+2x^77+2x^78+2x^79+1x^80+1x^86

The gray image is a linear code over GF(2) with n=512, k=12 and d=236.
This code was found by Heurico 1.16 in 0.422 seconds.