The generator matrix

 1  1  1  1  1  1
 0  2  0  0  4 14
 0  0  2  0  6  6
 0  0  0  2  2  4

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

Homogenous weight enumerator: w(x)=1x^0+96x^3+279x^4+1056x^5+5328x^6+1056x^7+279x^8+96x^9+1x^12

The gray image is a code over GF(2) with n=48, k=13 and d=12.
This code was found by Heurico 1.16 in 0.0119 seconds.