The generator matrix

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

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+192x^60+340x^61+672x^62+600x^63+778x^64+652x^65+790x^66+592x^67+784x^68+552x^69+516x^70+432x^71+492x^72+252x^73+232x^74+128x^75+110x^76+28x^77+28x^78+8x^79+9x^80+2x^82+2x^84

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 2.8 seconds.