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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+32x^56+46x^57+77x^58+100x^59+144x^60+142x^61+172x^62+234x^63+208x^64+246x^65+191x^66+138x^67+81x^68+54x^69+53x^70+30x^71+31x^72+20x^73+15x^74+10x^75+11x^76+4x^77+3x^78+4x^80+1x^106

The gray image is a linear code over GF(2) with n=256, k=11 and d=112.
This code was found by Heurico 1.16 in 0.449 seconds.