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

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+105x^64+108x^66+64x^67+235x^68+128x^69+182x^70+64x^71+27x^72+36x^74+29x^76+22x^78+18x^80+4x^82+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 0.414 seconds.