The generator matrix

 1  0  0  0  0  0  1  1  1  X  X  X  X  0  1  1  X  1  X  1  X  1  1  1  X  0  1  0  0  X  X  1  1  1  0  1  X  1  1  X  1  X  1  1
 0  1  0  0  0  0  0  0  0  1  0  1  1  1  1  1  X X+1  1  X  1  0  X  1  1  X X+1  1  0  1  1  1  0  0  1  1  1  X  1  X X+1  0  1 X+1
 0  0  1  0  0  0  0  0  0  0  1  1  1 X+1  1  X  1  X X+1 X+1 X+1  1 X+1  1  X  1  1  0  0  0 X+1  0  X X+1  1  X  0  0  X  0 X+1  X X+1 X+1
 0  0  0  1  0  0  0  1  1  1  1 X+1  X  0  0 X+1  X  X X+1 X+1  1  0  X  X  1 X+1  X X+1  1 X+1  1  0  X  X  0  1  X  0 X+1  1  X  1 X+1  0
 0  0  0  0  1  0  1  1  0  1  1  0 X+1  X  X  0  X X+1 X+1  0  0 X+1  X  1  1  0 X+1  0 X+1  0  1  1  1  X  X X+1  1  X  0  X  1  1  X  0
 0  0  0  0  0  1  1  0  1  1 X+1  0  X X+1  X  0  1  0  1  1  1  X  0 X+1  X  0  0  0  X  1  0 X+1  X X+1  0  1  X  1  1 X+1  X  1  X X+1
 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  0  X  X  X  X  0  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  0  X  X  0  0  0  X  X  X  0  X  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  0  0  X  0  X  0  X  X  0  X  0  X  0  X  X  0  0  X  0  0  X  0  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+68x^32+206x^33+392x^34+518x^35+695x^36+1060x^37+1341x^38+1602x^39+1815x^40+2132x^41+2370x^42+2540x^43+2750x^44+2692x^45+2597x^46+2400x^47+2109x^48+1626x^49+1208x^50+938x^51+644x^52+432x^53+251x^54+174x^55+101x^56+36x^57+30x^58+20x^59+6x^60+8x^61+3x^62+2x^64+1x^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 75.5 seconds.