The generator matrix

 1  1
 0 X+1

generates a code of length 2 over Z2[X]/(X^4) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+28x^1+198x^2+28x^3+1x^4

The gray image is a linear code over GF(2) with n=16, k=8 and d=4.
As d=5 is an upper bound for linear (16,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in -6.48e-008 seconds.