The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+83x^66+32x^67+55x^68+32x^69+18x^70+11x^72+19x^74+5x^76

The gray image is a linear code over GF(2) with n=272, k=8 and d=132.
This code was found by Heurico 1.16 in 0.138 seconds.