The generator matrix
1 0 1 1 1 X 1 1 1 1 0 X 1 1 1 1 X X 0 1
0 1 X+1 X 1 1 0 X X+1 1 1 1 0 X X+1 1 0 X X 0
generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+3x^20+8x^21+3x^22+1x^26
The gray image is a linear code over GF(2) with n=40, k=4 and d=20.
As d=20 is an upper bound for linear (40,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000864 seconds.