The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+40x^24+8x^25+54x^26+60x^27+154x^28+228x^29+386x^30+612x^31+881x^32+1124x^33+1100x^34+1164x^35+824x^36+620x^37+416x^38+204x^39+132x^40+68x^41+74x^42+8x^43+14x^44+14x^46+2x^48+4x^50

The gray image is a linear code over GF(2) with n=136, k=13 and d=48.
This code was found by Heurico 1.16 in 1.39 seconds.