The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+312x^60+208x^61+736x^62+328x^63+1066x^64+352x^65+1194x^66+348x^67+897x^68+316x^69+908x^70+260x^71+566x^72+168x^73+278x^74+52x^75+110x^76+12x^77+42x^78+4x^79+23x^80+8x^82+1x^84+2x^86

The gray image is a linear code over GF(2) with n=268, k=13 and d=120.
This code was found by Heurico 1.16 in 58.7 seconds.