The generator matrix
1 0 0 1 1 1 X 1 1 X 1 1 X 1 1 0 1 1 0 0
0 1 0 0 1 X+1 1 X X+1 1 X 1 1 X 1 1 0 X+1 1 0
0 0 1 1 X+1 0 X+1 1 X+1 1 X X X 1 1 X+1 X+1 X+1 X+1 1
0 0 0 X X X 0 0 0 X 0 X 0 X 0 X 0 X 0 X
generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+54x^18+43x^20+12x^22+3x^24+14x^26+1x^28
The gray image is a linear code over GF(2) with n=40, k=7 and d=18.
As d=18 is an upper bound for linear (40,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.259 seconds.