The generator matrix

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

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+178x^29+277x^30+482x^31+337x^32+658x^33+383x^34+606x^35+284x^36+430x^37+175x^38+182x^39+50x^40+14x^41+25x^42+10x^43+4x^46

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 3.85 seconds.