The generator matrix

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

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+17x^16+36x^17+41x^18+32x^19+24x^20+36x^21+19x^22+12x^23+18x^24+8x^25+3x^26+4x^27+4x^28+1x^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 0.00272 seconds.