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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+154x^64+48x^66+364x^68+208x^70+170x^72+74x^76+2x^80+2x^84+1x^128

The gray image is a linear code over GF(2) with n=276, k=10 and d=128.
This code was found by Heurico 1.16 in 0.329 seconds.