The generator matrix

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

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+113x^36+180x^38+321x^40+274x^42+360x^44+226x^46+249x^48+182x^50+83x^52+34x^54+21x^56+4x^60

The gray image is a linear code over GF(2) with n=88, k=11 and d=36.
This code was found by Heurico 1.16 in 0.362 seconds.