The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+139x^10+122x^11+589x^12+580x^13+1392x^14+1696x^15+2631x^16+3452x^17+3440x^18+4684x^19+3440x^20+3452x^21+2631x^22+1696x^23+1392x^24+580x^25+589x^26+122x^27+139x^28+1x^38

The gray image is a linear code over GF(2) with n=38, k=15 and d=10.
This code was found by Heurico 1.16 in 12 seconds.