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

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+166x^56+12x^57+284x^58+64x^59+430x^60+124x^61+456x^62+308x^63+526x^64+312x^65+474x^66+136x^67+282x^68+60x^69+194x^70+4x^71+133x^72+4x^73+84x^74+23x^76+10x^78+6x^80+2x^82+1x^100

The gray image is a linear code over GF(2) with n=256, k=12 and d=112.
This code was found by Heurico 1.16 in 1.29 seconds.