The generator matrix

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

generates a code of length 5 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+98x^4+64x^5+88x^6+5x^8

The gray image is a code over GF(2) with n=40, k=8 and d=16.
This code was found by Heurico 1.16 in 0.000172 seconds.