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  X  1  1  1  1  1  X  1  1  0  0  1  1  1  1 X^2  1  0  0  1  X  1  1  X  0  X X^2  1  1  1
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X  X  X  X X^2+X  X  0 X^2+X X^2  X X^2  X  0  X X^2 X^2+X  X  0 X^2+X X^2 X^2+X  0  0 X^2 X^2+X  X  X  X  0 X^2  X X^2+X  X  0 X^2  0 X^2 X^2+X X^2+X  X X^2  0 X^2 X^2+X X^2+X  0  X  0  X X^2  X  0  0 X^2
 0  0  X  0  0 X^2 X^2+X  X  X  X  X  X X^2+X  0  0  0 X^2 X^2 X^2+X  X X^2  0  0 X^2+X X^2 X^2  X X^2+X  0  X  X X^2+X  X X^2+X  0  0 X^2+X  X  X X^2+X X^2+X X^2+X X^2+X  X  X X^2+X X^2 X^2 X^2+X  X X^2  X  0 X^2+X X^2+X  0 X^2+X  X  0 X^2+X X^2 X^2 X^2  0
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  0  X  X X^2  X X^2 X^2+X  0 X^2+X  0 X^2  X X^2  X  X X^2  X  X  0  0 X^2  X X^2+X X^2+X X^2  X X^2+X  0 X^2+X  0 X^2  0 X^2 X^2  X X^2+X  0 X^2 X^2+X  X  X  X X^2  0  X X^2+X  0  0  X  0  X  X
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2 X^2  X X^2 X^2+X  X  X X^2 X^2 X^2+X  0 X^2+X  0 X^2+X X^2+X X^2+X  0 X^2+X  0  X  0 X^2  0 X^2+X  X  0  0 X^2+X X^2+X  0  X X^2 X^2+X  0 X^2  X X^2  0  X  0  X  X  0 X^2 X^2+X X^2  0  0 X^2  X  X X^2  0 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+64x^57+110x^58+134x^59+56x^60+228x^61+101x^62+358x^63+31x^64+364x^65+83x^66+208x^67+26x^68+92x^69+59x^70+56x^71+7x^72+20x^73+23x^74+10x^75+2x^76+8x^78+2x^79+4x^80+1x^104

The gray image is a linear code over GF(2) with n=256, k=11 and d=114.
This code was found by Heurico 1.16 in 13.2 seconds.