The generator matrix
1 1
0 X+1
generates a code of length 2 over Z4[X]/(X^2+2X+2) 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 code over GF(2) with n=16, k=8 and d=4.
This code was found by Heurico 1.16 in 1.05e-007 seconds.