The generator matrix

 1  0  0  0  0  1  1  1  0  1  X  X  1  1  1  X  1  1  X
 0  1  0  0  0  0  0  X  X  1  1  1  X  1  1  0  1  0  1
 0  0  1  0  0  X  1 X+1  1  0  1  1  1  X  0  1 X+1 X+1  0
 0  0  0  1  0 X+1  1  0  1  X X+1  1  0  0 X+1  X  X  0 X+1
 0  0  0  0  1  1  X  1  1 X+1  X  0  0  X  1 X+1  X X+1  X

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+92x^14+208x^16+224x^18+211x^20+180x^22+91x^24+16x^26+1x^28

The gray image is a linear code over GF(2) with n=38, k=10 and d=14.
As d=14 is an upper bound for linear (38,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 0.029 seconds.