The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  X  0  X  0  1  1  1  0  1  X  0  1  1  X  1  1  0  1  1  X  0  1  1  1  1  1  1
 0  1  0  0  0  1  1  1  X  0 X+1 X+1  1  1  X  1  1  X  0  1  X  1  1  1  X  1  0  X  0  1  1  1  1  0  0  1  1  X  X X+1  1 X+1 X+1
 0  0  1  0  1  1  0  1  0 X+1 X+1  X  X X+1  1  X  X  1  0 X+1  1  X  1  1 X+1  X  1  X  1  X  0  1  1  1  X X+1  X  0  X  X  0  0  0
 0  0  0  1  1  0  1  1  1  0  1  X X+1  0 X+1  1  1 X+1  1 X+1 X+1  1  0  X  1  0  0  X X+1 X+1  1 X+1 X+1  X  0  X  X  1  X  X  X  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  0  X  X  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  X  0  X  X  X  0  X  0  X  0  X  X  0  X  0  0  0  X  X  0  0  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  0  X  X  X  X  X  0  X  0  X  X  0  0  X  X  X  X  0  0  0  X  0  0  0  X  X
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  0  X  X  0  X  X  X  0  0  X  0  0  0  X  X  0  X  X  X  0  X  X  0  0  0  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+66x^34+88x^35+170x^36+238x^37+231x^38+218x^39+270x^40+324x^41+295x^42+304x^43+304x^44+368x^45+281x^46+212x^47+203x^48+188x^49+118x^50+72x^51+68x^52+34x^53+31x^54+2x^55+6x^56+1x^58+2x^60+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 1.16 in 1.33 seconds.