The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+45x^16+96x^21+33x^22+18x^24+32x^25+30x^30+1x^38

The gray image is a linear code over GF(2) with n=44, k=8 and d=16.
This code was found by Heurico 1.16 in -7.44e-008 seconds.