The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  1  X  0  0  1  1  X  0
 0  1  0  0  0  0  0  0  0  0  0  0  0  1  X  1  X  1  1  1  X  1
 0  0  1  0  0  0  0  0  0  1  1 X+1  X  0  0  X  1 X+1 X+1  1  0  X
 0  0  0  1  0  0  0  0  1  0 X+1 X+1  X  1  1  1 X+1  X  0  1  0  X
 0  0  0  0  1  0  0  0  1  1  0  1 X+1 X+1  0  X  X X+1  1  0  1 X+1
 0  0  0  0  0  1  0  1  0 X+1 X+1  X  0 X+1 X+1 X+1  1  1  0  X  0  1
 0  0  0  0  0  0  1  1 X+1  X  0  1  X  0 X+1  1 X+1 X+1  1  X  X  0
 0  0  0  0  0  0  0  X  X  0  X  0  X  X  0  X  0  X  0  0  X  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+114x^13+286x^14+468x^15+845x^16+1270x^17+1728x^18+2542x^19+3300x^20+3726x^21+4096x^22+3846x^23+3186x^24+2662x^25+1868x^26+1210x^27+820x^28+408x^29+210x^30+126x^31+40x^32+12x^33+4x^34

The gray image is a linear code over GF(2) with n=44, k=15 and d=13.
This code was found by Heurico 1.11 in 7.79 seconds.