The generator matrix
1 0 1 X 1 1 1 1 1 1
0 1 X 1 X+1 1 0 X X+1 1
generates a code of length 10 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+12x^10+2x^12+1x^16
The gray image is a linear code over GF(2) with n=20, k=4 and d=10.
As d=10 is an upper bound for linear (20,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000157 seconds.