The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  X  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  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  X  0  0  0  0  X  X  X  X  X  X  X  0  0  X  0  0  X  X  X  X  0  X  0  X  X  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0  X  X  X  X  0  X  X  X  X  0  X  0  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  X  0  X  X  X  0  0  0  0  0  0  0  0  X  0  X  0  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  X  X  0  X  0  X  0  X  X  X  0  X  0  0  X  X  X  X  X  0  0  X  X  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  X  0  X  0  X  0  X  0  0  0  X  0  X  X  0  X  0  0  0  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  X  0  X  0  0  0  X  X  X  0  0  0  X  X  0  X  0  X  X  X  X  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  0  X  0  0  X  0  0  0  0  X  X  X  X  X  X  X  0  0  X  X  X  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  0  X  0  0  X  X  0  0  X  0  X  X  0  0  X  X  X  0  0  0  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  0  0  0  0  0  X  0  0  0  0  X  X  0  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+136x^32+298x^36+515x^40+512x^42+1168x^44+512x^46+542x^48+274x^52+117x^56+20x^60+1x^80

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 2.2 seconds.