The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  1  1  1  X  1  1  X  1  1  1  0  X  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  0  X  X  X  0  X  X  X  X  0  X  X  X  X  X  X  X  X  0  X  0  0  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  0  0  X  X  0  0  0  X  0  X  X  X  0  0  X  0  X  X  X  X  X  X
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  X  X  X  0  X  X  0  0  0  0  X  0  X  0  0  0  0  X  X  0  X  X
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  0  X  X  X  X  0  0  0  X  0  0  X  0  0  0  X  0  X  X
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  0  0  X  X  X  X  X  X  X  X  X  0  0  X  0  X  X  X  X  0  0  X
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  X  0  X  0  X  X  X  X  0  X  X  0  0  0  X  0  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  0  0  X  0  X  0  0  0  X  0  X  0  0  X  X
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  X  X  0  X  X  0  X

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+39x^34+72x^36+100x^38+152x^40+164x^42+163x^44+144x^46+85x^48+39x^50+27x^52+20x^54+10x^56+6x^58+1x^60+1x^68

The gray image is a linear code over GF(2) with n=86, k=10 and d=34.
This code was found by Heurico 1.16 in 0.382 seconds.