The generator matrix

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

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+230x^56+484x^57+728x^58+924x^59+1039x^60+1308x^61+1398x^62+1372x^63+1509x^64+1522x^65+1353x^66+1302x^67+1015x^68+756x^69+594x^70+362x^71+222x^72+126x^73+79x^74+22x^75+12x^76+12x^77+6x^78+2x^79+4x^80+2x^82

The gray image is a linear code over GF(2) with n=256, k=14 and d=112.
This code was found by Heurico 1.13 in 3.81 seconds.