The generator matrix

 1  0  0  1  1  1  X  1  1  1  1  1  X  0  0  1  1  1  1  1
 0  1  0  1  0 X+1  1  0  X  1 X+1  X  1  1  0  X  X  0  0  0
 0  0  1  1  1  0  1  X  1 X+1  X  1  0  1  1 X+1 X+1  1  0  0
 0  0  0  X  0  X  0  X  X  X  0  0  0  X  X  0  0  X  0  0
 0  0  0  0  X  0  0  0  X  X  X  0  X  X  0  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+47x^16+76x^18+42x^20+40x^22+24x^24+12x^26+14x^28

The gray image is a linear code over GF(2) with n=40, k=8 and d=16.
As d=16 is an upper bound for linear (40,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 0.00296 seconds.