The generator matrix

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

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+133x^36+128x^38+349x^40+256x^42+354x^44+256x^46+308x^48+128x^50+97x^52+29x^56+8x^60+1x^64

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 0.464 seconds.