The generator matrix

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

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+78x^31+166x^32+334x^33+541x^34+790x^35+1058x^36+1218x^37+1443x^38+1800x^39+2269x^40+2486x^41+2548x^42+2772x^43+2851x^44+2578x^45+2370x^46+2058x^47+1622x^48+1294x^49+849x^50+602x^51+420x^52+250x^53+171x^54+80x^55+53x^56+30x^57+14x^58+12x^59+7x^60+2x^61+1x^64

The gray image is a linear code over GF(2) with n=86, k=15 and d=31.
This code was found by Heurico 1.16 in 72.7 seconds.