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  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  1  1  0 X^2  0  1  1  X  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X  0 X^2  X  X  0 X^2  X  X X^2+X X^2 X^2+X  0 X^2+X  X X^2  0 X^2 X^2+X  X  0 X^2 X^2 X^2 X^2 X^2+X  X  X X^2+X X^2 X^2  X X^2 X^2+X X^2  X X^2+X  0  0  0  0  X  X X^2+X X^2+X X^2  X  X X^2+X X^2+X  X  0 X^2
 0  0  X  0  X  X  X X^2  0 X^2 X^2+X X^2+X  X  X X^2 X^2  0 X^2+X  0  X  X  X  0  0 X^2+X X^2+X X^2+X X^2  0 X^2  0  X  X X^2+X X^2 X^2 X^2 X^2  0  0 X^2+X  0  X  0 X^2+X  X X^2+X  X X^2+X  X  X X^2+X X^2  0  0 X^2  X  X X^2+X  X  0  0 X^2+X X^2
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2+X  X  0  X  0 X^2 X^2+X X^2+X  0 X^2+X X^2  0 X^2+X  0  X  X X^2 X^2+X X^2+X  0 X^2  0 X^2  0 X^2 X^2  0 X^2+X X^2+X  X  X  X  X  X  X X^2  0 X^2  0 X^2+X X^2+X X^2 X^2 X^2 X^2 X^2  0  0  X X^2+X  X X^2 X^2
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  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 58.

Homogenous weight enumerator: w(x)=1x^0+28x^58+76x^59+63x^60+60x^61+102x^62+130x^63+135x^64+120x^65+100x^66+84x^67+47x^68+12x^69+24x^70+20x^71+8x^72+8x^75+1x^76+2x^78+2x^79+1x^116

The gray image is a linear code over GF(2) with n=256, k=10 and d=116.
This code was found by Heurico 1.16 in 0.218 seconds.