The generator matrix
1 1
0 X^2+X
generates a code of length 2 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 1.
Homogenous weight enumerator: w(x)=1x^0+12x^1+102x^2+12x^3+1x^4
The gray image is a code over GF(2) with n=16, k=7 and d=4.
This code was found by Heurico 1.16 in -1.01e-007 seconds.