The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  X  X  1  0  0  1
 0  1  0  0  0  0  0  0  0  0  0  1  1  X  1  X  1  1  0
 0  0  1  0  0  0  0  0  1  1  X  1  X  1  1  0  1  1  0
 0  0  0  1  0  0  0  0  1  X X+1  1  0  0 X+1  X X+1  0  0
 0  0  0  0  1  0  0  0  1 X+1  1  0  1  X X+1 X+1  0  1  0
 0  0  0  0  0  1  0  1  0  1  X X+1  X  1  0  0 X+1  0  0
 0  0  0  0  0  0  1  1 X+1  1  0  X  0 X+1 X+1  1 X+1  X  0
 0  0  0  0  0  0  0  X  X  0  0  0  X  X  0  0  X  0  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+133x^10+130x^11+607x^12+548x^13+1392x^14+1728x^15+2583x^16+3484x^17+3476x^18+4604x^19+3476x^20+3484x^21+2583x^22+1728x^23+1392x^24+548x^25+607x^26+130x^27+133x^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 1.11 in 3.81 seconds.