The generator matrix

 1  0  0  1  4 10
 0  1  0  2  1  1
 0  0  1  1  2  6

generates a code of length 6 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+201x^4+690x^5+2317x^6+684x^7+198x^8+2x^9+3x^10

The gray image is a code over GF(2) with n=48, k=12 and d=16.
This code was found by Heurico 1.16 in -8.39e-008 seconds.