The generator matrix

 1  0  1  1  1 X^2+X  1  1  0 X^2+X  1  1  1 X^2  1  1  1  0  X X^2+X  1  1  1  1  1  1 X^2  1  0  1  1  1  1  X  1  1  X  1  1  1  0 X^2  1 X^2+X  1  1 X^2+X  1  1  1  X  X  1  1  1  1 X^2  1  1  1  X  1 X^2  X
 0  1  1  0  1  1  X X^2+X+1  1  1 X^2+X+1 X^2+X  1  1  0  X X^2+1  1  1  1 X^2+X+1 X+1  0 X^2+1  0  1  1 X^2+X  1  0 X^2+X X^2+X  1  1 X^2+X+1  1  1  1  0 X^2  1  1  0  1 X+1 X^2  1 X^2+X+1 X^2  0  1  1  X X^2+X+1  0 X+1  1 X^2+X+1  1  1  1 X^2+X  1 X^2
 0  0  X  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2  X  X X^2+X  X  X X^2+X X^2+X  X  X  X  X  X  X X^2+X X^2 X^2+X X^2  X  X  X X^2 X^2 X^2+X X^2+X  0 X^2  0 X^2+X  0 X^2+X  X X^2+X X^2  X X^2  X  0  X  0  0
 0  0  0  X  0  0  X X^2  X X^2+X  X X^2 X^2+X  X  X X^2 X^2 X^2  0  X X^2+X X^2  X  X  0 X^2+X  X  X  0  0  X  0 X^2 X^2  X X^2 X^2+X X^2 X^2  0 X^2  0  0  X  0 X^2 X^2+X  0 X^2+X  0  X X^2+X X^2+X X^2  X  X  0  X  0  0  0  X  X  X
 0  0  0  0  X  0  0  X  X X^2+X X^2 X^2 X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2+X  0  X  0  X X^2+X  X X^2  X X^2 X^2+X X^2 X^2+X  0  0  0  0 X^2 X^2  X  X  0  X X^2  X X^2+X X^2  X  X X^2+X X^2+X  0 X^2 X^2+X  0 X^2+X  0  0  X X^2+X X^2+X X^2 X^2 X^2+X  0 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 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+162x^56+88x^57+492x^58+224x^59+682x^60+600x^61+888x^62+652x^63+930x^64+572x^65+714x^66+632x^67+596x^68+208x^69+352x^70+92x^71+171x^72+4x^73+70x^74+39x^76+12x^78+8x^80+3x^84

The gray image is a linear code over GF(2) with n=256, k=13 and d=112.
This code was found by Heurico 1.16 in 4.38 seconds.