The generator matrix
1 0 1 1 1
0 1 X+1 X 0
generates a code of length 5 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+7x^4+6x^6+2x^8
The gray image is a linear code over GF(2) with n=10, k=4 and d=4.
As d=4 is an upper bound for linear (10,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 4.91e-005 seconds.