The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+50x^9+181x^10+456x^11+861x^12+1404x^13+2379x^14+3750x^15+5297x^16+6780x^17+7690x^18+7992x^19+7594x^20+6544x^21+5326x^22+3844x^23+2462x^24+1538x^25+785x^26+336x^27+169x^28+68x^29+23x^30+6x^31

The gray image is a linear code over GF(2) with n=38, k=16 and d=9.
This code was found by Heurico 1.11 in 11.6 seconds.