The generator matrix

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

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+16x^14+54x^15+131x^16+184x^17+257x^18+344x^19+365x^20+416x^21+501x^22+476x^23+380x^24+376x^25+261x^26+136x^27+110x^28+48x^29+19x^30+14x^31+4x^32+2x^34+1x^36

The gray image is a linear code over GF(2) with n=44, k=12 and d=14.
This code was found by an older version of Heurico in 0 seconds.