The generator matrix

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

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+80x^31+127x^32+64x^34+160x^35+32x^36+16x^39+28x^40+4x^48

The gray image is a linear code over GF(2) with n=136, k=9 and d=62.
This code was found by Heurico 1.16 in 4.45 seconds.