The generator matrix

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

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+236x^64+184x^66+264x^68+152x^70+106x^72+48x^74+24x^76+3x^80+5x^88+1x^104

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 3.74 seconds.