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

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+23x^58+16x^59+64x^60+144x^61+64x^62+272x^63+31x^64+272x^65+8x^66+8x^68+16x^69+16x^70+16x^71+16x^72+16x^73+16x^74+16x^75+8x^76+1x^122

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 0.235 seconds.