The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+46x^22+123x^24+28x^25+146x^26+108x^27+327x^28+320x^29+1129x^30+672x^31+2587x^32+920x^33+3530x^34+920x^35+2667x^36+672x^37+1085x^38+320x^39+348x^40+108x^41+158x^42+28x^43+77x^44+43x^46+12x^48+6x^50+1x^52+1x^54+1x^56

The gray image is a linear code over GF(2) with n=136, k=14 and d=44.
This code was found by Heurico 1.16 in 6.67 seconds.