The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+18x^69+3x^70+4x^71+3x^72+2x^73+1x^78

The gray image is a linear code over GF(2) with n=272, k=5 and d=138.
This code was found by Heurico 1.16 in 0.134 seconds.