The generator matrix

 1  0  0  0  1  1
 0  1  0  0  2  5
 0  0  1  0  3  1
 0  0  0  1  1  2

generates a code of length 6 over Z16 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+256x^3+2199x^4+13440x^5+33744x^6+13440x^7+2199x^8+256x^9+1x^12

The gray image is a code over GF(2) with n=48, k=16 and d=12.
This code was found by Heurico 1.16 in 0.843 seconds.