The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  1  1  X  X  0  1
 0  1  1  0  1  1  0 X+1  1  0 X+1  1  0  0  X  X  X  X  0  0
 0  0  X  0  0  0  0  X  0  X  X  X  0  X  X  0  X  X  X  0
 0  0  0  X  0  0  X  X  0  X  0  X  0  X  0  X  0  X  0  0
 0  0  0  0  X  0  X  0  X  X  X  X  0  0  0  0  X  X  0  0
 0  0  0  0  0  X  0  X  X  X  0  X  X  0  0  X  X  X  X  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+37x^16+48x^17+26x^18+16x^20+64x^21+14x^22+10x^24+16x^25+22x^26+2x^30

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 9.54e-008 seconds.