The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+69x^14+122x^15+243x^16+346x^17+472x^18+590x^19+827x^20+920x^21+883x^22+1040x^23+781x^24+708x^25+561x^26+272x^27+177x^28+72x^29+60x^30+22x^31+19x^32+2x^33+3x^34+2x^35

The gray image is a linear code over GF(2) with n=44, k=13 and d=14.
This code was found by Heurico 1.10 in 0.515 seconds.