The generator matrix

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

generates a code of length 35 over Z2[X]/(X^3) who�s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+6x^34+44x^35+6x^36+1x^38+4x^39+1x^40+1x^46

The gray image is a linear code over GF(2) with n=140, k=6 and d=68.
This code was found by Heurico 1.16 in 0.0147 seconds.