The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+60x^31+106x^32+92x^33+74x^34+56x^35+38x^36+24x^37+28x^38+12x^39+7x^40+12x^41+2x^42

The gray image is a linear code over GF(2) with n=136, k=9 and d=62.
This code was found by Heurico 1.11 in 0.016 seconds.