The generator matrix

 1  0  0  0  0  0  0  1  1  1  X  1  X  X  1  1  1  0  1  X  X  1  1  0  1  1  1  1  1  0  0  1  1  X  0  0  X  1  X  X  1  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  X  1 X+1 X+1 X+1  1  1  1  1  1  1  1  0  1  X  1  1  X  1  X
 0  0  1  0  0  0  0  0  0  0  0  0  X  X  1 X+1  1  1 X+1  1  1  0  X  1  1  1  X  X  X  X  0 X+1  0  1 X+1  1  1 X+1  1  0  0 X+1  0
 0  0  0  1  0  0  0  0 X+1  X  1  1  X  1  1  X  X  1  X  0  X X+1  X X+1  X  X  X X+1 X+1 X+1  1 X+1  1 X+1  0 X+1  0 X+1  X X+1  1  0  0
 0  0  0  0  1  0  0  0  1 X+1  1  0  1  1  X  0 X+1  1 X+1  X  1 X+1  0 X+1  0  0  X  X  0 X+1 X+1  X  0  0  1  1  X  1  1 X+1 X+1 X+1  0
 0  0  0  0  0  1  0  1  0  1  1  1  0  X  0  X  1 X+1 X+1 X+1  0 X+1  0 X+1 X+1  X  0 X+1  0  X  X  X X+1 X+1  X  X X+1  1 X+1 X+1  1  0  1
 0  0  0  0  0  0  1  1 X+1  0 X+1  X  1  1  0  1  0  1  1  1  X X+1 X+1  0 X+1  0 X+1  X  1  0  1  X  1  0  1 X+1 X+1 X+1  0 X+1  1  0  0
 0  0  0  0  0  0  0  X  X  X  X  0  X  0  X  0  0  0  X  X  X  0  X  X  0  X  0  X  X  X  0  0  0  0  0  X  0  0  0  X  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+72x^31+209x^32+342x^33+537x^34+762x^35+930x^36+1226x^37+1519x^38+1858x^39+2229x^40+2412x^41+2695x^42+2838x^43+2739x^44+2636x^45+2369x^46+1966x^47+1620x^48+1254x^49+899x^50+590x^51+404x^52+298x^53+157x^54+102x^55+53x^56+24x^57+13x^58+2x^59+7x^60+3x^62+2x^63

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 94.7 seconds.