The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  0  0  X  0  0  X  X  0
 0  1  0  1  0  1  1  0  X  1 X+1  1  1  0  1  1  1  1  0  X  0  0
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  1  0  X  1 X+1  1  1  0  X
 0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  X  0  X  0  0  0  X
 0  0  0  0  X  0  0  0  X  0  0  X  X  X  0  X  X  0  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  0  X  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  X  0  0  X
 0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  0  X  X  X  X  X

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+206x^16+128x^18+560x^20+256x^22+576x^24+128x^26+176x^28+17x^32

The gray image is a linear code over GF(2) with n=44, k=11 and d=16.
This code was found by Heurico 1.16 in 0.111 seconds.