The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+56x^32+48x^33+172x^34+202x^35+355x^36+470x^37+670x^38+920x^39+1180x^40+1520x^41+1661x^42+1844x^43+1656x^44+1548x^45+1226x^46+944x^47+685x^48+464x^49+302x^50+178x^51+131x^52+46x^53+55x^54+8x^55+30x^56+9x^58+2x^60+1x^70

The gray image is a linear code over GF(2) with n=172, k=14 and d=64.
This code was found by Heurico 1.16 in 11.4 seconds.