The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+28x^12+104x^14+90x^16+120x^18+396x^20+528x^22+392x^24+240x^26+84x^28+8x^30+29x^32+24x^34+4x^36

The gray image is a linear code over GF(2) with n=44, k=11 and d=12.
This code was found by Heurico 1.16 in 0.0795 seconds.