The generator matrix

 1  0  0  1  2  1
 0  1  0  1  0  0
 0  0  1  1  0  0
 0  0  0 12 12  0
 0  0  0  0  8  0
 0  0  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+102x^2+560x^3+2431x^4+12240x^5+34868x^6+12240x^7+2431x^8+560x^9+102x^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 0.27 seconds.