The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1 X^2  1 X^2  1  1 X^2+X  1  1  1  1  1  1  1 X^2  1  X  X  1  1  X  X
 0  1  1  0 X^2+X+1  1  X X^2+X+1  1 X+1  0  1 X^2+X+1  1  X  1 X^2+1  0  1 X^2+X+1 X^2+X  1 X+1 X^2+1 X^2+X  0  1 X^2+1 X^2  1 X^2 X^2+X  0  0
 0  0  X  0 X^2+X X^2  0  0  0 X^2  X X^2 X^2+X X^2+X X^2+X X^2+X  X  0 X^2+X X^2 X^2+X  0  X  0 X^2 X^2+X X^2+X  0  0 X^2 X^2+X  X  X  X
 0  0  0  X  0 X^2 X^2+X  X  X X^2  X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2  X X^2+X X^2 X^2+X  0 X^2 X^2  0  X  X  0 X^2+X X^2 X^2  X
 0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 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+96x^29+152x^30+188x^31+261x^32+226x^33+255x^34+254x^35+201x^36+186x^37+98x^38+48x^39+48x^40+14x^41+3x^42+6x^43+1x^44+6x^45+4x^46

The gray image is a linear code over GF(2) with n=136, k=11 and d=58.
This code was found by Heurico 1.16 in 0.118 seconds.