The generator matrix

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

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+43x^26+90x^27+162x^28+384x^29+370x^30+792x^31+599x^32+1256x^33+735x^34+1348x^35+632x^36+848x^37+328x^38+296x^39+120x^40+72x^41+53x^42+34x^43+22x^44+6x^46+1x^50

The gray image is a linear code over GF(2) with n=136, k=13 and d=52.
This code was found by Heurico 1.16 in 1.69 seconds.