The generator matrix

 1  1  1  1  1  1  1  1  2  1  1  2  2  4  2  2  4  2  2  2
 0  8  0  8  0  8  0  8  8  0  8  0  8  8  0  8  0  0  8  0

generates a code of length 20 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+25x^20+4x^22+2x^26

The gray image is a code over GF(2) with n=160, k=5 and d=80.
This code was found by Heurico 1.16 in 0.00247 seconds.