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  X  1  1  X  X  1  X  1  1  1  1  X  0  1  1  X  X  1  1  1  X  1  0  1  X  1  X X^2  0  X  0  X  0
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2+X X^2 X^2+X  0 X^2  X  X X^2  X  0  X X^2+X X^2 X^2+X  0  X  0 X^2+X X^2 X^2+X  X  0 X^2+X X^2 X^2+X  X  0  X  X X^2 X^2+X  X X^2  X X^2+X  0  X  X  0  X X^2+X X^2
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X X^2  0 X^2+X X^2+X X^2 X^2+X X^2  0 X^2  X X^2  X  X  X  0 X^2  0  X X^2 X^2  X X^2+X X^2+X X^2+X  X X^2  X X^2+X  0 X^2  0  0  X X^2  X  X X^2+X  X  0  X X^2 X^2+X X^2+X  X X^2  0  X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2+X  0  X X^2  X  X  0  0  X X^2 X^2+X X^2+X  X  X X^2+X X^2+X X^2+X  0  0 X^2  0 X^2 X^2  X  0  X X^2  X  X X^2  X  0 X^2 X^2 X^2  0 X^2 X^2  0  X  X  0  X  0 X^2  0 X^2
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  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+186x^56+24x^57+306x^58+52x^59+403x^60+156x^61+440x^62+316x^63+518x^64+228x^65+442x^66+140x^67+314x^68+100x^69+198x^70+4x^71+134x^72+4x^73+76x^74+34x^76+10x^78+9x^80+1x^92

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 3.89 seconds.