The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+15x^16+32x^19+15x^22+1x^38

The gray image is a linear code over GF(2) with n=38, k=6 and d=16.
This code was found by Heurico 1.16 in 0.00121 seconds.