The generator matrix

 1  0  1  1  1  4
 0  1  1  0  3  1
 0  0  2  0  2  4
 0  0  0  2  2  6

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

Homogenous weight enumerator: w(x)=1x^0+96x^3+471x^4+3360x^5+8528x^6+3360x^7+471x^8+96x^9+1x^12

The gray image is a code over GF(2) with n=48, k=14 and d=12.
This code was found by Heurico 1.16 in 0.0329 seconds.