The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+188x^28+236x^29+586x^30+640x^31+976x^32+936x^33+1138x^34+932x^35+1033x^36+588x^37+438x^38+216x^39+187x^40+32x^41+46x^42+4x^43+15x^44

The gray image is a linear code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.16 in 1.45 seconds.