The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+62x^17+122x^18+94x^19+103x^20+108x^21+80x^22+108x^23+93x^24+70x^25+82x^26+54x^27+25x^28+16x^29+4x^30+2x^32

The gray image is a linear code over GF(2) with n=44, k=10 and d=17.
This code was found by Heurico 1.16 in 14.1 seconds.