The generator matrix
1 1 1 1
0 2 0 0
0 0 2 0
0 0 0 2
generates a code of length 4 over GR(16,4) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+12x^4+54x^8+876x^12+81x^16
The gray image is a code over GF(4) with n=16, k=5 and d=4.
This code was found by Heurico 1.16 in -3.62e-008 seconds.