The generator matrix

 1  0  1  2  2
 0  1  1  0  8
 0  0  2  2  0
 0  0  0  4  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+109x^2+640x^3+3602x^4+7680x^5+3602x^6+640x^7+109x^8+1x^10

The gray image is a code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.0178 seconds.