The generator matrix

 1  0  0  0  1  1  1  X  0  1  1 X^2  1  X  1  1  1  X  1  1  0  1  1 X^2+X  1 X^2  1  1  1  1 X^2+X  1 X^2  1
 0  1  0  0  1 X^2 X+1  1  X  1  0  1 X+1  1  0 X^2+X+1 X^2  1 X^2+X X^2+1  1  1  X  X X+1  X X^2+X+1 X^2+X+1  X X^2+X+1  1 X^2+1 X^2 X^2
 0  0  1  0  1 X^2+1 X^2 X^2+1  1 X+1 X^2+X+1  1  X X^2 X^2  1 X^2+X  1 X^2+1  X  X  0  0  0 X^2+X+1  1  X X+1 X+1 X^2+1  X X^2  1 X^2
 0  0  0  1 X^2  1 X^2+1 X^2+X+1 X+1  1 X^2+X X^2+X X^2  1 X^2+X+1 X+1 X^2+X+1 X^2+1 X^2+1  X X+1 X^2+1 X^2+X  1 X+1  1  X X^2 X+1 X^2+X  1  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+154x^29+301x^30+478x^31+467x^32+442x^33+462x^34+596x^35+386x^36+300x^37+225x^38+154x^39+64x^40+46x^41+12x^42+4x^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 1.11 in 0.125 seconds.