The generator matrix

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

generates a code of length 43 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+65x^34+100x^35+184x^36+232x^37+232x^38+266x^39+267x^40+292x^41+287x^42+292x^43+287x^44+296x^45+275x^46+260x^47+206x^48+180x^49+139x^50+96x^51+69x^52+24x^53+25x^54+10x^55+10x^56+1x^66

The gray image is a linear code over GF(2) with n=86, k=12 and d=34.
This code was found by Heurico 1.16 in 1.26 seconds.