The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  1  1  0  X  0  X  1  1  0  1
 0  1  0  0  0  1  1  1  X  X X+1  0  1 X+1  1  X  1  1  X X+1  1  0
 0  0  1  0  1  1  0 X+1  X  1 X+1  X  0 X+1 X+1  1  0 X+1  X  1  1  0
 0  0  0  1  1  0 X+1 X+1  0  X X+1  1  X  1  1 X+1 X+1  0 X+1  X  1  0
 0  0  0  0  X  0  X  X  X  X  0  0  X  X  X  0  0  X  X  X  X  0
 0  0  0  0  0  X  0  X  0  X  0  X  X  X  0  X  X  0  X  0  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+37x^16+60x^17+86x^18+92x^19+101x^20+96x^21+88x^22+120x^23+66x^24+92x^25+80x^26+44x^27+50x^28+8x^29+2x^34+1x^36

The gray image is a linear code over GF(2) with n=44, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0286 seconds.