The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  1  1  1  X  0  1  1  1
 0  1  0  0  0  0  0  0  0  0  X  1  1  1  1  1 X+1  1  0
 0  0  1  0  0  0  0  0  0  0 X+1  1 X+1  X  X  0  1  1  0
 0  0  0  1  0  0  0  1  1  1  1  0  X  X  1 X+1  1  0  0
 0  0  0  0  1  0  1  1  0  1  0  X X+1  0  0  1  X  0  0
 0  0  0  0  0  1  1  0  1  1  0  X  1 X+1 X+1  X  1  0  0
 0  0  0  0  0  0  X  0  0  X  X  0  0  0  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  X  X  0  0  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  X  0  X  0  0  X  0  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+137x^10+114x^11+597x^12+624x^13+1414x^14+1656x^15+2537x^16+3344x^17+3506x^18+4908x^19+3506x^20+3344x^21+2537x^22+1656x^23+1414x^24+624x^25+597x^26+114x^27+137x^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 13.6 seconds.