The generator matrix

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

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+46x^34+98x^35+176x^36+228x^37+209x^38+264x^39+324x^40+310x^41+293x^42+298x^43+274x^44+272x^45+291x^46+274x^47+217x^48+176x^49+132x^50+84x^51+58x^52+36x^53+20x^54+6x^55+6x^56+2x^57+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 1.25 seconds.