The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+102x^29+378x^30+438x^31+523x^32+468x^33+457x^34+418x^35+454x^36+336x^37+272x^38+130x^39+68x^40+20x^41+21x^42+6x^43+2x^44+2x^45

The gray image is a linear code over GF(2) with n=136, k=12 and d=58.
This code was found by Heurico 1.16 in 0.286 seconds.