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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+68x^57+149x^58+202x^59+223x^60+294x^61+418x^62+484x^63+550x^64+666x^65+764x^66+710x^67+686x^68+704x^69+602x^70+424x^71+336x^72+284x^73+165x^74+126x^75+99x^76+74x^77+66x^78+36x^79+24x^80+22x^81+10x^82+2x^83+2x^86+1x^96

The gray image is a linear code over GF(2) with n=268, k=13 and d=114.
This code was found by Heurico 1.16 in 5.92 seconds.