The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+49x^68+4x^70+4x^72+4x^74+1x^76+1x^80

The gray image is a linear code over GF(2) with n=272, k=6 and d=136.
This code was found by Heurico 1.16 in 0.0889 seconds.