The generator matrix

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

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+524x^59+1052x^60+1916x^61+1704x^62+2384x^63+1902x^64+2288x^65+1504x^66+1320x^67+743x^68+548x^69+216x^70+184x^71+37x^72+48x^73+4x^75+9x^76

The gray image is a linear code over GF(2) with n=512, k=14 and d=236.
This code was found by Heurico 1.16 in 8.75 seconds.