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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+302x^64+256x^66+64x^68+256x^70+32x^72+64x^76+48x^80+1x^128

The gray image is a linear code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 0.279 seconds.