The generator matrix

 1  0  0  0  1  1  1  X  1  1  0  1  1  X  1  1  1  0  1
 0  1  0  0  X  X  X  0 X+1  1  X  1  1  1  0 X+1  1  1  0
 0  0  1  0  0 X+1  1  1  0  X  1  X  1  0  X  X  0  1  1
 0  0  0  1  1 X+1  0  1  X X+1  X  1  X  0  0  1  1  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+36x^16+78x^17+39x^18+18x^20+36x^21+18x^22+9x^24+14x^25+7x^26

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 0.00263 seconds.