The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  0  1  X  1  1  1  1  X  X  X  X  1  1  0  1  0  0  0  0  X  1  1  1  0  X  1  1  X
 0  1  0  0  0  1  1  1  0  0  1 X+1  1  0  1  X  1  X  1  1  0  1  1  0  X  X  1  X X+1  1  0  1  1  X  1  1  X  0 X+1  1  1 X+1  1  1
 0  0  1  0  1  1  0  1  0  1  1  0  0  1 X+1  X  1 X+1  X  1  0  0  X  1  1  0  0  1 X+1  X  1 X+1  X  1  X  X  1  0  1  1  1 X+1  0  1
 0  0  0  1  1  0  1  1  1  0  1  0 X+1  1  X X+1 X+1  X  0  X  0  1 X+1  1  0  1 X+1  0  X  0  1  X  1 X+1  1  0 X+1  0 X+1  X  1  1 X+1  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  0  0  X  X  X  0  0  X  0  X  X  0  X  X  0  X  0  0  0  0  0  X  X  X  0  0  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  X  0  0  X  0  X  0  0  0  X  X  X  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  0  0  X  0  X  X  0  0  X  0  X  X  X  X  0  X  0  X  X  0  0  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  0  X  X  0  0  0  X  X  X  0  X  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  X  0  X  X  X  X  0  0  0  X  0  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  0  X  X  0  0  0  X  X  X  0  X  0  X  X  X  0  X  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  X  0  X  X  0  X  X  X  X  0  X  X  X  0  0  0  0  X  0  X  X  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+278x^32+560x^34+1556x^36+2308x^38+3888x^40+4730x^42+5856x^44+4962x^46+4130x^48+2308x^50+1422x^52+440x^54+244x^56+50x^58+28x^60+2x^62+3x^64+2x^68

The gray image is a linear code over GF(2) with n=88, k=15 and d=32.
This code was found by Heurico 1.16 in 73.6 seconds.