The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  0  1  1  1  1  1  X  X  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  1  1  1  X  X  1  X  1  1  1 X+1
 0  0  1  0  0  0  0 X+1  X  1  1  0  X X+1 X+1  1  X  1  X  1  1 X+1
 0  0  0  1  0  0  0  1 X+1  1  0  1  1 X+1 X+1 X+1  X  0 X+1  X  0  0
 0  0  0  0  1  0  1  0  1  1  1  X  1 X+1 X+1  0  0  X  X  X  0  1
 0  0  0  0  0  1  1 X+1  0 X+1  X X+1  1 X+1  1  X  X  1  0  1  0  1
 0  0  0  0  0  0  X  X  X  X  0  X  0  X  0  0  X  0  0  0  X  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+71x^14+110x^15+235x^16+368x^17+471x^18+642x^19+753x^20+898x^21+965x^22+974x^23+851x^24+690x^25+485x^26+294x^27+195x^28+86x^29+56x^30+28x^31+13x^32+6x^33

The gray image is a linear code over GF(2) with n=44, k=13 and d=14.
This code was found by Heurico 1.16 in 1.55 seconds.