The generator matrix

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

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+102x^58+378x^59+277x^60+578x^61+278x^62+482x^63+340x^64+426x^65+208x^66+256x^67+157x^68+208x^69+86x^70+138x^71+51x^72+66x^73+30x^74+26x^75+6x^76+2x^77

The gray image is a linear code over GF(2) with n=256, k=12 and d=116.
This code was found by Heurico 1.11 in 0.297 seconds.