The generator matrix

 1  0  0  0  0  0  0  1  1  1  X  1  1  1  1  1  1  0  0  0  0  0  X  X  1  X  0  1  1  X  X  0  X  1  1  X  X  1  0  0  0  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  X  1  X  1
 0  0  1  0  0  0  0  0  0  0  0  0  X  X  1  1 X+1  1  X  1  1  1  X  X  1  1  1 X+1  X X+1  X  0  X  1 X+1  X  1  X  1  X X+1  X  1
 0  0  0  1  0  0  0  0  1  1  1  0  1 X+1  1 X+1  X  1  0 X+1  1  1  1  1 X+1  1  0  0  X  0  X X+1  0  X  X X+1  0 X+1  1  0  0  X  0
 0  0  0  0  1  0  0  0  1  X X+1  1 X+1  0 X+1 X+1  X  0  1  0  X  1 X+1  1  X  0  X  X  1  X X+1  0  1  1  0  X  1  X  0  1  1  1  0
 0  0  0  0  0  1  0  1  0  1 X+1 X+1  0  X  1  1  X X+1 X+1  0  1  1  X  0  X  X  X  1  X X+1  0 X+1  1  1  0 X+1  1 X+1  0  0  1  X  0
 0  0  0  0  0  0  1  1 X+1  0  1  X  X  0  0  1 X+1 X+1  1 X+1  0  0  1  0 X+1  0  X  1  1  0  1  X  1 X+1 X+1  1  X X+1 X+1  1 X+1  X  0
 0  0  0  0  0  0  0  X  X  0  0  0  0  X  X  0  X  0  0  X  X  0  X  X  X  0  X  0  0  0  X  0  0  X  0  X  X  0  X  0  0  X  X

generates a code of length 43 over Z2[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+70x^31+213x^32+350x^33+526x^34+730x^35+933x^36+1272x^37+1530x^38+1794x^39+2240x^40+2588x^41+2648x^42+2638x^43+2752x^44+2648x^45+2417x^46+2058x^47+1602x^48+1246x^49+886x^50+534x^51+381x^52+320x^53+172x^54+110x^55+64x^56+24x^57+12x^58+2x^59+6x^60+1x^62

The gray image is a linear code over GF(2) with n=86, k=15 and d=31.
This code was found by Heurico 1.11 in 31 seconds.