The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  1  0  1  1  0  1  0  X  X
 0  1  1  0  1  1  0 X+1  1  1  0  X  1  0  0  1  X  1  1  1
 0  0  X  0  0  0  0  0  0  X  X  X  0  0  X  0  X  X  X  0
 0  0  0  X  0  0  0  X  0  X  X  0  X  0  X  X  X  0  0  0
 0  0  0  0  X  0  0  0  X  X  0  0  X  0  X  0  X  X  0  X
 0  0  0  0  0  X  0  X  X  X  0  0  0  X  0  X  X  0  0  X
 0  0  0  0  0  0  X  X  0  X  0  X  X  X  0  0  X  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+120x^16+64x^18+144x^20+64x^22+116x^24+3x^32

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 1.16 in 4.16 seconds.