The generator matrix

 1  1  1  1  1  1
 0  2  0  0  0  4
 0  0  2  0  0  4
 0  0  0  2  0  4
 0  0  0  0  2  4

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

Homogenous weight enumerator: w(x)=1x^0+114x^2+512x^3+2735x^4+7168x^5+44476x^6+7168x^7+2735x^8+512x^9+114x^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 0.341 seconds.