The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+130x^26+228x^27+753x^28+888x^29+1832x^30+2600x^31+3235x^32+4368x^33+4328x^34+4552x^35+3594x^36+2776x^37+1716x^38+776x^39+564x^40+160x^41+182x^42+36x^43+45x^44+4x^46

The gray image is a linear code over GF(2) with n=136, k=15 and d=52.
This code was found by Heurico 1.16 in 18.5 seconds.