The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  X  1  X  0  1  1  X  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  1  X  1  1 X+1  X  X X+1  1
 0  0  1  0  0  0  0  0  0 X+1  1  X  1  0  X X+1  1  X  X X+1  X  X
 0  0  0  1  0  0  0  0 X+1  1  X  X  1 X+1  1  0  1  0  1  X X+1 X+1
 0  0  0  0  1  0  0  0  1  0  1  1 X+1  X  0  1 X+1  1  X  0 X+1  1
 0  0  0  0  0  1  0  1  0  1  0 X+1 X+1  X  1  X  1  1 X+1 X+1  1  X
 0  0  0  0  0  0  1  1 X+1  X  1  0 X+1  0  X  0 X+1  0  1  X  1  0
 0  0  0  0  0  0  0  X  X  0  0  X  0  X  X  X  X  0  0  0  0  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+108x^13+287x^14+482x^15+801x^16+1258x^17+1855x^18+2534x^19+3221x^20+3788x^21+3990x^22+3776x^23+3342x^24+2632x^25+1822x^26+1288x^27+794x^28+392x^29+235x^30+110x^31+32x^32+14x^33+3x^34+2x^35+1x^36

The gray image is a linear code over GF(2) with n=44, k=15 and d=13.
This code was found by Heurico 1.16 in 24.1 seconds.