The generator matrix

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

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+75x^34+140x^35+214x^36+322x^37+332x^38+428x^39+524x^40+536x^41+617x^42+574x^43+629x^44+654x^45+598x^46+590x^47+476x^48+442x^49+347x^50+286x^51+162x^52+88x^53+70x^54+30x^55+38x^56+6x^57+9x^58+3x^60+1x^64

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 5.52 seconds.