The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+40x^36+60x^37+92x^38+158x^39+200x^40+190x^41+213x^42+230x^43+196x^44+214x^45+136x^46+96x^47+55x^48+42x^49+67x^50+24x^51+16x^52+6x^53+3x^54+2x^55+4x^56+2x^59+1x^62

The gray image is a linear code over GF(2) with n=172, k=11 and d=72.
This code was found by Heurico 1.16 in 0.206 seconds.