The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  X  1 X^2+X  1  X X^2  1  1  X  1  1  0  0  1  1  1  1  X  0  1 X^2+X  1  X X^2  1  1 X^2  1  1  1 X^2  X  1  1  X X^2 X^2+X  1  1  1  X X^2+X  1  1  0  1  1 X^2+X  1  X X^2  X  1
 0  1  0  0  1 X^2+X+1  1 X^2  0 X^2 X^2+X+1  1 X+1  1  1 X^2+X  1  X  X  1  X X^2+1  X  1 X+1  1  0 X+1  1  X X+1  1  X  1 X^2 X^2+1  0  1  0 X^2+1 X^2+1  1  1  1  X  1  1 X^2  0 X+1  X X^2+X  1 X^2+X  1  1 X^2+1  0  1  0  1  1  1  0
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  X X+1 X^2+1  1  X X^2+X  0 X^2 X+1 X^2+X  1 X+1  0  1 X^2+X+1  0 X+1  1 X^2+1 X^2+1  X  0  1 X^2 X^2+1 X^2+X+1 X^2+X+1 X^2+X+1  X X^2+X+1 X^2+X X^2+1 X^2+X+1 X^2  1  1 X^2+X  X X^2+X+1  1  0 X^2+1  0  0 X^2 X^2+X+1 X^2+X X^2  1 X^2+X+1  X  0
 0  0  0  X  X X^2+X X^2 X^2+X  0  0  X X^2  X  0 X^2+X  0  0 X^2 X^2 X^2 X^2+X  X  0 X^2 X^2+X  0  0 X^2 X^2+X  X X^2  X  X X^2+X X^2+X X^2 X^2  0 X^2+X  0 X^2+X  X  X  X  0  X  X  X  X X^2+X  0  X X^2+X  X  0  X  0 X^2 X^2 X^2  0  X  X  0
 0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2  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+30x^56+244x^57+284x^58+558x^59+572x^60+784x^61+598x^62+828x^63+760x^64+728x^65+499x^66+676x^67+485x^68+460x^69+233x^70+220x^71+63x^72+76x^73+41x^74+22x^75+7x^76+12x^77+9x^78+2x^80

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 3.5 seconds.