The generator matrix

 1  1  1  1  1  1
 0 12  0  0  8 12
 0  0 12  0 12 12
 0  0  0 12  4  8

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

Homogenous weight enumerator: w(x)=1x^0+16x^3+39x^4+48x^5+816x^6+48x^7+39x^8+16x^9+1x^12

The gray image is a code over GF(2) with n=48, k=10 and d=12.
This code was found by Heurico 1.16 in 0.00058 seconds.