The generator matrix

 1  0  1
 0  1 2a+2
 0  0  1

generates a code of length 3 over GR(16,4) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+36x^3+9x^4+432x^6+216x^7+27x^8+1728x^9+1296x^10+324x^11+27x^12

The gray image is a code over GF(4) with n=12, k=6 and d=3.
This code was found by Heurico 1.16 in -1.01e-007 seconds.