The generator matrix

 1  1  1  1  1  1
 0  2  0  0  0  8
 0  0  2  0  0  0
 0  0  0 12  0  0
 0  0  0  0 12  0
 0  0  0  0  0  4

generates a code of length 6 over Z16 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+20x^1+162x^2+708x^3+2159x^4+6440x^5+46556x^6+6440x^7+2159x^8+708x^9+162x^10+20x^11+1x^12

The gray image is a code over GF(2) with n=48, k=16 and d=4.
This code was found by Heurico 1.16 in 0.249 seconds.