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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+289x^60+472x^61+820x^62+808x^63+1289x^64+1088x^65+1524x^66+1336x^67+1544x^68+1184x^69+1464x^70+996x^71+1186x^72+788x^73+690x^74+352x^75+273x^76+112x^77+98x^78+28x^79+18x^80+4x^81+10x^82+6x^84+2x^86+2x^88

The gray image is a linear code over GF(2) with n=272, k=14 and d=120.
This code was found by Heurico 1.13 in 10.3 seconds.