The generator matrix

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

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+175x^32+278x^34+861x^36+1036x^38+2045x^40+2180x^42+3073x^44+2370x^46+2087x^48+1118x^50+743x^52+176x^54+199x^56+8x^58+27x^60+2x^62+5x^64

The gray image is a linear code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.16 in 22.5 seconds.