The generator matrix

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

generates a code of length 5 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+41x^2+120x^3+406x^4+2960x^5+406x^6+120x^7+41x^8+1x^10

The gray image is a code over GF(2) with n=40, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00185 seconds.