The generator matrix

 1  1  1  1  1  1
 0  2  0  2  0  0
 0  0  2  2  0  0
 0  0  0  8  0  0
 0  0  0  0  8  0

generates a code of length 6 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+40x^2+48x^3+151x^4+336x^5+2944x^6+336x^7+151x^8+48x^9+40x^10+1x^12

The gray image is a code over GF(2) with n=48, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0019 seconds.