The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+66x^15+132x^16+218x^17+275x^18+254x^19+392x^20+448x^21+434x^22+530x^23+434x^24+292x^25+261x^26+170x^27+92x^28+64x^29+21x^30+4x^31+5x^32+2x^33+1x^38

The gray image is a linear code over GF(2) with n=44, k=12 and d=15.
This code was found by Heurico 1.10 in 0.172 seconds.