The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  0  1  1  1  0  1  0  1  0  1  X  1  0  1  1  1  X  1  0  1  X  1  1  X  0  0  0  1  1  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  0  1 X+1  0 X+1  1  0  1 X+1  1  X  1 X+1  1  1  0  X  1  1  1  0  1 X+1 X+1  X  1  X  X  X  0  0  0
 0  0  X  0  0  0  0  0  0  0  X  0  X  0  0  X  X  0  X  0  X  0  X  0  0  X  X  X  0  X  0  X  0  0  0  X  0  X  0  X  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  0  0  0  X  0  0  X  0  X  X  X  X  0  X  X  X  0  0  0  X  X  0  0  0  X  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  X  0  X  X  X  X  0  0  0  0  X  0  X  0  X  X  0  0  0  X  0  X  X  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  0  0  X  X  X  0  X  X  X  0  0  0  X  0  X  X  X  X  0  X  X  X  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  0  X  X  X  X  0  X  0  0  X  X  0  X  X  X  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  X  X  0  X  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  0  X  X  X  0  X  X  0  0  0  0  X  0  X  X  X  X  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  0  X  X  0  0  0  X  0  X  X  X  X  0  X  X  0  0  X  X  0  0  X  X  0  X  0  X  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+55x^32+52x^34+38x^35+157x^36+118x^37+148x^38+192x^39+234x^40+280x^41+253x^42+372x^43+257x^44+404x^45+277x^46+328x^47+200x^48+184x^49+179x^50+86x^51+95x^52+38x^53+83x^54+8x^55+22x^56+27x^58+3x^60+3x^62+1x^66+1x^70

The gray image is a linear code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 1.59 seconds.