The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+84x^11+218x^12+342x^13+587x^14+910x^15+1261x^16+1690x^17+1996x^18+2118x^19+2040x^20+1718x^21+1354x^22+922x^23+538x^24+334x^25+156x^26+62x^27+38x^28+12x^29+3x^30

The gray image is a linear code over GF(2) with n=38, k=14 and d=11.
This code was found by Heurico 1.16 in 7.72 seconds.