The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+189x^30+196x^31+395x^32+212x^33+255x^34+208x^35+184x^36+96x^37+181x^38+44x^39+60x^40+12x^41+13x^42+2x^46

The gray image is a linear code over GF(2) with n=136, k=11 and d=60.
This code was found by Heurico 1.16 in 0.351 seconds.