The generator matrix

 1  0  0  1  1  1  0  1  1  1  0  1  X  0  1  1  1  1  1
 0  1  0  1  0  1  1  0  0  1  1 X+1  1  0  X  X  X  0  0
 0  0  1  1  1  0  1  0  1  1  X  0 X+1  1  X  1  1  0  0
 0  0  0  X  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0
 0  0  0  0  X  0  0  0  0  0  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  X  X  0  X  0  X  0  X
 0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  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+31x^10+149x^12+128x^13+327x^14+384x^15+595x^16+896x^17+934x^18+1280x^19+946x^20+896x^21+622x^22+384x^23+330x^24+128x^25+123x^26+25x^28+11x^30+2x^32

The gray image is a linear code over GF(2) with n=38, k=13 and d=10.
This code was found by Heurico 1.16 in 0.596 seconds.