The generator matrix

 1  1  2  1  1  1
 0  2  2  0  0  0
 0  0  4  0  4  0
 0  0  0 12  4  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+38x^2+64x^3+223x^4+1472x^5+4596x^6+1472x^7+223x^8+64x^9+38x^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 0.00934 seconds.