The generator matrix

 1  0  1  2  1  1
 0  1  1  0  0  0
 0  0  2  2  0  0
 0  0  0  4  0  4
 0  0  0  0 12  4
 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+106x^2+384x^3+2895x^4+11904x^5+34956x^6+11904x^7+2895x^8+384x^9+106x^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 0.299 seconds.