The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1
 0  X  0  0  0  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  0  0  0  X  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  X  X  X  X  0  X  X  X  0  X  0  X  0  0  X  0  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  X  0  0  0  0  0  0  X  X  0  0  X  X  0  0  0  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  X  0  X  0  X  0  X  0  0  0  X  X  X  0  X  0  0  0  0  X  0  0  X  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  0  X  0  0  X  0  0  0  0  X  X  0  0  0  X  X  0  X  0  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  X  X  0  X  0  X  0  0  X  0  X  0  0  X  0  0  X  X  0  0  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  0  X  X  0  0  X  0  X  X  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  0  0  0  X  X  0  X  0  0  X  0  X  0  X  X  X  X  X  0  X  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  X  X  0  0  0  X  0  0  0  X  0  0  X  X  0  0  X  0  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  0  X  0  X  0  X  X  X  0  X  0  0  X  X  0  0  0  0  X  X  0  0  0  X  X  X  0

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+48x^28+62x^30+133x^32+193x^34+238x^36+530x^38+565x^40+1581x^42+1608x^44+1146x^46+1076x^48+347x^50+270x^52+166x^54+102x^56+55x^58+44x^60+16x^62+10x^64+1x^72

The gray image is a linear code over GF(2) with n=88, k=13 and d=28.
This code was found by Heurico 1.16 in 14 seconds.