The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+55x^34+100x^35+169x^36+228x^37+294x^38+466x^39+573x^40+772x^41+947x^42+982x^43+1012x^44+804x^45+530x^46+426x^47+293x^48+204x^49+140x^50+62x^51+59x^52+40x^53+16x^54+12x^55+5x^56+1x^58+1x^66

The gray image is a linear code over GF(2) with n=172, k=13 and d=68.
This code was found by Heurico 1.16 in 3.02 seconds.