The generator matrix

 1  0  0  0  1  1  1  1  0  1  0  1  1  X  0  X  X  0  0
 0  1  0  0  0  0  1  1  1  X  1  1  X  0  0  1  1  1  1
 0  0  1  0  0  1  1  0 X+1  1  X X+1  0  1  1  0  X X+1 X+1
 0  0  0  1  1  1  0 X+1 X+1  0  1 X+1 X+1  1  0  X  1 X+1  0
 0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  0  X  X  0
 0  0  0  0  0  X  0  X  0  X  0  0  X  X  0  0  X  X  X
 0  0  0  0  0  0  X  X  X  0  0  0  X  X  0  X  0  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+46x^13+111x^14+134x^15+188x^16+206x^17+210x^18+246x^19+230x^20+218x^21+176x^22+130x^23+90x^24+42x^25+14x^26+2x^27+2x^28+1x^30+1x^32

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 18.9 seconds.