The generator matrix

 1  0  0  1
 0  1  0  1
 0  0  1 3a+3

generates a code of length 4 over GR(16,4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+72x^6+18x^8+384x^9+432x^10+1368x^12+1152x^13+648x^14+21x^16

The gray image is a code over GF(4) with n=16, k=6 and d=6.
This code was found by Heurico 1.16 in 0 seconds.