The generator matrix

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

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+258x^32+712x^34+1623x^36+2384x^38+3731x^40+4754x^42+5519x^44+4964x^46+4089x^48+2476x^50+1389x^52+504x^54+253x^56+74x^58+29x^60+4x^62+4x^64

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 seconds.