The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+14x^20+1x^24

The gray image is a linear code over GF(2) with n=38, k=4 and d=20.
As d=20 is an upper bound for linear (38,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000862 seconds.