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

generates a code of length 69 over Z2[X]/(X^3) who�s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+13x^66+32x^67+50x^68+320x^69+50x^70+32x^71+13x^72+1x^138

The gray image is a linear code over GF(2) with n=276, k=9 and d=132.
This code was found by Heurico 1.16 in 0.164 seconds.