The generator matrix

 1  1  1  2  8  1  1
 0  2  0  6  2  2  4
 0  0 12  8 12  4  4

generates a code of length 7 over Z16 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+26x^5+130x^6+206x^7+119x^8+22x^9+6x^10+2x^11

The gray image is a code over GF(2) with n=56, k=9 and d=20.
This code was found by Heurico 1.16 in 0.00067 seconds.