The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+137x^62+232x^63+240x^64+268x^65+202x^66+188x^67+161x^68+148x^69+114x^70+76x^71+82x^72+52x^73+47x^74+36x^75+17x^76+12x^77+11x^78+12x^79+11x^80+1x^82

The gray image is a linear code over GF(2) with n=268, k=11 and d=124.
This code was found by Heurico 1.16 in 0.308 seconds.