The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+74x^4+168x^5+552x^6+144x^7+77x^8+8x^9

The gray image is a code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 0.000866 seconds.