The generator matrix

 1  0  0  0  0  0  0  1  1  1  X  1  1  1  1  1  0  1  X  X  1  X  1  X  1  1  X  1  1  X  X  1  1  X  0  0  1  1  1  1  1  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  1  1  1  1  1  1 X+1 X+1  1  X  1 X+1 X+1 X+1  X X+1  1  0  X
 0  0  1  0  0  0  0  0  0  0  0  0  X  X  1  1  1 X+1  1  X X+1  1  1  X  1  1 X+1  0  1 X+1  X X+1  0 X+1  1 X+1  0 X+1  0  0  X  0  1  0
 0  0  0  1  0  0  0  0  1  1  1  0  1 X+1  X  0  0 X+1 X+1  X  1  X X+1  1  0  0  1  X  1  0  1  1 X+1  0  X  X  1 X+1  0  0 X+1 X+1  0  0
 0  0  0  0  1  0  0  0  1  X X+1  1  1  0 X+1  0 X+1  1  1  1  X X+1  0 X+1  X  X  1  X  0  X  X X+1  1  X  0 X+1 X+1 X+1  1 X+1  X  0  0  1
 0  0  0  0  0  1  0  1  0  1 X+1 X+1  X  0 X+1  X  0  1  1  1  1  1  0  0 X+1  0  1  X X+1 X+1  0  X  X  0 X+1 X+1 X+1  0 X+1  0 X+1  1  1  0
 0  0  0  0  0  0  1  1 X+1  0  1  X  0  X  1  1  X  1  0 X+1  0  0 X+1  1  0  1  X  1 X+1  0  X  0  0  X X+1 X+1  1  1  0 X+1  X X+1 X+1  0
 0  0  0  0  0  0  0  X  X  0  0  0  0  X  X  0  X  0  X  0  X  0  X  X  0  X  0  0  0  X  X  X  0  0  0  0  X  X  X  X  X  0  X  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+119x^32+192x^33+374x^34+554x^35+701x^36+996x^37+1199x^38+1518x^39+1927x^40+2162x^41+2445x^42+2656x^43+2690x^44+2760x^45+2632x^46+2366x^47+1979x^48+1626x^49+1244x^50+908x^51+629x^52+410x^53+275x^54+172x^55+125x^56+44x^57+17x^58+18x^59+20x^60+2x^61+6x^62+1x^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 1.11 in 32.4 seconds.