The generator matrix

 1  1  1  1  2  1
 0  2  0  2  0  0
 0  0  2  2  0  0
 0  0  0  4 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+54x^2+176x^3+703x^4+1872x^5+10772x^6+1872x^7+703x^8+176x^9+54x^10+1x^12

The gray image is a code over GF(2) with n=48, k=14 and d=8.
This code was found by Heurico 1.16 in 0.0298 seconds.