The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 0 0 1 X 1 1 1 1 1 X X X 1 1 1 0 1 1 0 1 1 X 0 1 1 0 1 0 1
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 1 X+1 1 1 X X 1 0 X 1 X X+1 1 X 1 0 1 0 X+1 1 1 1 X+1 1 1 X X 0
0 0 1 0 0 0 0 0 X X 1 1 1 X 1 X+1 X+1 X+1 X X+1 1 0 X+1 1 X 1 X 1 1 X 1 0 1 X X+1 1 1 X X 0 X 0 0
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X 1 1 1 X X 1 X+1 1 0 X+1 1 0 X+1 X+1 0 1 X+1 X+1 0 0 0 1 1 1 X 0 1 0
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 X X+1 X+1 0 X+1 1 X+1 X 0 1 0 0 X 0 X X+1 1 0 X 1 1 1 X X X+1 X 0 X+1 0
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 0 0 0 0 X+1 X X X+1 1 1 X+1 0 X+1 X 0 1 X 1 0 X 0 1 X+1 1 X+1 X 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+68x^34+120x^35+167x^36+214x^37+238x^38+270x^39+313x^40+258x^41+260x^42+288x^43+269x^44+334x^45+255x^46+268x^47+220x^48+182x^49+156x^50+72x^51+76x^52+36x^53+14x^54+6x^55+10x^56+1x^62

The gray image is a linear code over GF(2) with n=86, k=12 and d=34.
This code was found by Heurico 1.10 in 0.469 seconds.