The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  0  X  1  X  1  0  1  0  1  0
 0  1  0  0  0  1  1  1  X  0 X+1  1  1  1 X+1  1  X  0 X+1  1 X+1  1
 0  0  1  0  1  1  0  1  0 X+1  1  X  1  0  1  X  0  1  X  1 X+1 X+1
 0  0  0  1  1  0  1 X+1  1  X X+1  0  X  1  1  X  0  1  0  X  X X+1
 0  0  0  0  X  0  0  X  0  X  X  X  0  X  X  0  X  0  0  0  0  0
 0  0  0  0  0  X  0  0  X  X  X  0  0  0  0  X  0  X  X  0  X  0
 0  0  0  0  0  0  X  0  X  X  0  X  0  0  X  X  0  0  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+118x^16+312x^18+380x^20+416x^22+420x^24+280x^26+100x^28+16x^30+5x^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 0.142 seconds.