The generator matrix

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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+26x^53+91x^54+124x^55+247x^56+394x^57+502x^58+824x^59+710x^60+1538x^61+1062x^62+2216x^63+1067x^64+2184x^65+901x^66+1596x^67+824x^68+850x^69+385x^70+328x^71+172x^72+110x^73+112x^74+28x^75+30x^76+18x^77+12x^78+4x^79+16x^80+5x^82+4x^84+2x^86+1x^88

The gray image is a linear code over GF(2) with n=256, k=14 and d=106.
This code was found by Heurico 1.16 in 83.8 seconds.