The generator matrix

 1  1  2  2  1
 0  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+1x^4+26x^5+2x^6+2x^7

The gray image is a code over GF(2) with n=40, k=5 and d=16.
This code was found by Heurico 1.16 in 7.2e-005 seconds.