The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+44x^13+114x^14+148x^15+157x^16+212x^17+237x^18+220x^19+242x^20+212x^21+179x^22+140x^23+78x^24+44x^25+11x^26+4x^27+2x^28+3x^30

The gray image is a linear code over GF(2) with n=38, k=11 and d=13.
This code was found by Heurico 1.16 in 0.104 seconds.