The generator matrix

 1  0  0  1  1  1  0  1  1  X  1  0  0  1  1  X  1  1  1
 0  1  0  1  0  1  1  0  X  1  1  1  0  X  X  0  1  0  0
 0  0  1  1  1  0  1  0  1 X+1  1  0  1  0 X+1  1  X X+1  1
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  X  X  0
 0  0  0  0  X  0  0  0  X  0  X  X  X  X  0  0  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  0  X
 0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  0  X  0  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+109x^14+153x^16+268x^18+220x^20+178x^22+70x^24+20x^26+4x^28+1x^30

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 46.3 seconds.