The generator matrix

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

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+78x^16+96x^18+32x^22+48x^24+1x^32

The gray image is a linear code over GF(2) with n=38, k=8 and d=16.
As d=16 is an upper bound for linear (38,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in -3.81e-008 seconds.