The generator matrix

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

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+71x^16+106x^17+38x^18+44x^20+110x^21+52x^22+12x^24+38x^25+38x^26+2x^29

The gray image is a linear code over GF(2) with n=40, k=9 and d=16.
As d=16 is an upper bound for linear (40,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9.
This code was found by Heurico 1.10 in 0 seconds.