The generator matrix

1 0 0 0 0 1 1 1 X 1 1 0 0 1 X 0 X 0 0 1 X X
0 1 0 0 0 0 0 0 0 1 1 1 X 1 X 1 1 X 0 1 X 0
0 0 1 0 0 0 1 1 1 0 X X 1 X 1 0 X 1 1 0 X 0
0 0 0 1 0 1 0 X+1 1 1 0 X+1 1 X 1 X+1 0 1 X X+1 1 0
0 0 0 0 1 1 X+1 X 1 X 1 1 0 X X X X+1 0 1 X+1 X+1 X
0 0 0 0 0 X X 0 0 0 0 X X X X X 0 0 X 0 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+185x^16+188x^18+440x^20+412x^22+422x^24+276x^26+96x^28+20x^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 1.10 in 0.047 seconds.