The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^22+7x^24+2x^26

The gray image is a linear code over GF(2) with n=44, k=4 and d=22.
This code was found by Heurico 1.16 in 0.000844 seconds.