The generator matrix

1 0 0 0 0 1 1 1 X 1 1 X 1 1 1 1 1 1 0 X 0 1
0 1 0 0 0 0 0 X X 1 1 1 X+1 X 1 X X+1 X+1 0 0 X 0
0 0 1 0 0 1 X 1 1 0 X+1 X 0 X X X+1 X+1 0 X 1 1 0
0 0 0 1 0 1 X+1 0 1 X X+1 0 1 1 X X 0 X 1 X 0 0
0 0 0 0 1 X 1 1 X+1 1 X+1 0 1 0 X 0 X+1 X 0 X X 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+29x^16+56x^17+114x^18+108x^19+56x^20+84x^21+122x^22+104x^23+70x^24+112x^25+70x^26+44x^27+32x^28+4x^29+14x^30+4x^32

The gray image is a linear code over GF(2) with n=44, k=10 and d=16.
This code was found by Heurico 1.10 in 0.015 seconds.