The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+8x^5+31x^6+176x^7+31x^8+8x^9+1x^14

The gray image is a code over GF(2) with n=56, k=8 and d=20.
This code was found by Heurico 1.16 in 0.000367 seconds.