The generator matrix

 1  0  1  1  1
 0  1 11  0  0
 0  0 12  0  4
 0  0  0 12  4
 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+69x^2+144x^3+1338x^4+5088x^5+1338x^6+144x^7+69x^8+1x^10

The gray image is a code over GF(2) with n=40, k=13 and d=8.
This code was found by Heurico 1.16 in 0.00565 seconds.