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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+13x^72+2x^76

The gray image is a linear code over GF(2) with n=272, k=4 and d=144.
This code was found by Heurico 1.16 in 0.134 seconds.