The generator matrix

 1  0  1  2  1  1
 0  1  1  4  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+56x^2+144x^3+247x^4+1392x^5+4512x^6+1392x^7+247x^8+144x^9+56x^10+1x^12

The gray image is a code over GF(2) with n=48, k=13 and d=8.
This code was found by Heurico 1.16 in 0.00531 seconds.