The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  X  X  X  0  0  1  X  1  0  0  X
 0  1  0  0  0  0  0  0  0  1  1  1  X  1  X  1  1  X  1  1  1  0
 0  0  1  0  0  0  1  1  1  1 X+1  0  1  X  1  X  1  1 X+1 X+1  X  0
 0  0  0  1  0  1  1  X X+1  0 X+1  1 X+1  X  1 X+1 X+1 X+1  0 X+1  0  0
 0  0  0  0  1  1  X X+1  1  0  1  1  0  1  0  X  X  0  1  X  0  0
 0  0  0  0  0  X  0  X  0  X  0  0  X  X  X  0  0  0  X  X  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+159x^16+248x^18+402x^20+412x^22+448x^24+224x^26+134x^28+12x^30+8x^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 0.117 seconds.