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  X  X  0  X X^2  0  X  X  0  X X^2  0  X  X  X X^2  0  X  0  X  0  X X^2  X X^2  X  X  X  X  X  X  X  1  1  1  1  1
 0  X  0  X  0  0 X^2+X X^2+X  0  0  X  X  0  0 X^2+X X^2+X X^2 X^2  X X^2+X X^2 X^2 X^2+X  X X^2 X^2  X X^2+X X^2 X^2 X^2+X  X X^2  X  X X^2+X  X  0 X^2  X  X X^2+X  X  0  0  X X^2+X  X  X  0 X^2  X  X X^2+X  X  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  X X^2+X  0
 0  0  X  X  0 X^2+X X^2+X  0 X^2 X^2+X X^2+X X^2 X^2  X  X X^2 X^2  X  X  0 X^2  X X^2+X X^2  0 X^2+X X^2+X X^2  0 X^2+X  X  0  X  X X^2  0  X  X  X  X X^2  0  X  X  0 X^2+X  X X^2+X X^2+X X^2+X  X X^2  0 X^2  0  X  X X^2 X^2  0  0 X^2 X^2  0  0  X  X  0  0
 0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2  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+15x^66+108x^67+16x^68+32x^69+16x^70+12x^71+15x^72+1x^74+32x^75+8x^77

The gray image is a linear code over GF(2) with n=276, k=8 and d=132.
This code was found by Heurico 1.16 in 0.196 seconds.