The generator matrix
1 0 1 X 1 1 1 1
0 1 X 1 X+1 1 0 X
generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+13x^8+2x^12
The gray image is a linear code over GF(2) with n=16, k=4 and d=8.
As d=8 is an upper bound for linear (16,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000104 seconds.