The generator matrix

 1  0  0  1  2  1
 0  1  0  1  4  0
 0  0  1  1  0  0
 0  0  0  2  2  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+124x^2+864x^3+3751x^4+12064x^5+31928x^6+12064x^7+3751x^8+864x^9+124x^10+1x^12

The gray image is a code over GF(2) with n=48, k=16 and d=8.
This code was found by Heurico 1.16 in 0.194 seconds.