The generator matrix

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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+156x^57+386x^58+454x^59+813x^60+640x^61+881x^62+594x^63+755x^64+612x^65+698x^66+552x^67+549x^68+338x^69+321x^70+156x^71+114x^72+52x^73+72x^74+18x^75+8x^76+10x^77+8x^78+2x^79+2x^82

The gray image is a linear code over GF(2) with n=256, k=13 and d=114.
This code was found by Heurico 1.16 in 2.69 seconds.