The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+289x^16+456x^20+262x^24+16x^28

The gray image is a linear code over GF(2) with n=40, k=10 and d=16.
As d=16 is an upper bound for linear (40,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.10 in 0.078 seconds.