The generator matrix

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

generates a code of length 43 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+110x^30+152x^31+437x^32+692x^33+1027x^34+1366x^35+1843x^36+2288x^37+2982x^38+3834x^39+4446x^40+5166x^41+5311x^42+5674x^43+5514x^44+5304x^45+4620x^46+3848x^47+3298x^48+2372x^49+1873x^50+1302x^51+867x^52+500x^53+302x^54+198x^55+98x^56+58x^57+29x^58+10x^59+8x^60+4x^61+2x^62

The gray image is a linear code over GF(2) with n=86, k=16 and d=30.
This code was found by Heurico 1.11 in 122 seconds.