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

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+111x^60+4x^61+200x^62+52x^63+223x^64+120x^65+292x^66+152x^67+262x^68+132x^69+166x^70+52x^71+133x^72+56x^74+50x^76+22x^78+18x^80+1x^84+1x^112

The gray image is a linear code over GF(2) with n=268, k=11 and d=120.
This code was found by Heurico 1.16 in 0.428 seconds.