The generator matrix

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

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+16x^69+3x^70+8x^71+3x^72+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.