The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  0

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+68x^8+46x^10+264x^12+276x^14+662x^16+1024x^17+746x^18+2048x^19+720x^20+1024x^21+632x^22+292x^24+290x^26+40x^28+52x^30+1x^32+6x^34

The gray image is a linear code over GF(2) with n=38, k=13 and d=8.
This code was found by Heurico 1.16 in 0.989 seconds.