The generator matrix

 1  0  1  1  1  4  1  1  1  1
 0  1  1  0  3  1  8  9  6  8
 0  0  2  0  2  4  2  4  2  0
 0  0  0  2  2  6  6  2  2  4
 0  0  0  0  8  0  0  8  8  0
 0  0  0  0  0  8  0  8  8  8

generates a code of length 10 over Z16 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+36x^5+212x^6+852x^7+3674x^8+14216x^9+27544x^10+14216x^11+3704x^12+852x^13+180x^14+36x^15+13x^16

The gray image is a code over GF(2) with n=80, k=16 and d=20.
This code was found by Heurico 1.16 in 0.831 seconds.