The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+60x^13+188x^14+294x^15+447x^16+676x^17+898x^18+1264x^19+1587x^20+1766x^21+1897x^22+1848x^23+1645x^24+1274x^25+973x^26+680x^27+377x^28+254x^29+135x^30+74x^31+39x^32+2x^33+5x^34

The gray image is a linear code over GF(2) with n=44, k=14 and d=13.
This code was found by Heurico 1.10 in 1.83 seconds.