The generator matrix

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

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+82x^34+122x^35+219x^36+336x^37+375x^38+386x^39+519x^40+558x^41+551x^42+614x^43+574x^44+718x^45+622x^46+518x^47+483x^48+442x^49+355x^50+248x^51+239x^52+122x^53+59x^54+32x^55+13x^56+3x^58+1x^82

The gray image is a linear code over GF(2) with n=88, k=13 and d=34.
This code was found by Heurico 1.16 in 5.58 seconds.