The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  X  0  1  0  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  X  X X+1  1  X  0  0
 0  0  1  0  0  0  1  1  1  1  1  X  X  1  1 X+1 X+1  1  0
 0  0  0  1  0  1  1  0  1  0  1 X+1  1  0  X  X X+1  0  0
 0  0  0  0  1  1  0  1  1  0  1  1 X+1  1  1  X  1  1  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  X  0  0  X  X  0  X  X  0  X  0  X  0
 0  0  0  0  0  0  0  X  0  X  0  X  0  X  0  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  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+63x^10+84x^11+210x^12+390x^13+623x^14+928x^15+1316x^16+1688x^17+1874x^18+2008x^19+1904x^20+1668x^21+1306x^22+992x^23+616x^24+344x^25+223x^26+84x^27+46x^28+6x^29+7x^30+3x^32

The gray image is a linear code over GF(2) with n=38, k=14 and d=10.
This code was found by Heurico 1.16 in 4.62 seconds.