The generator matrix

 1  0  0  1  2
 0  1  0  1  8
 0  0  1  1  0
 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+141x^2+1152x^3+6386x^4+17408x^5+6386x^6+1152x^7+141x^8+1x^10

The gray image is a code over GF(2) with n=40, k=15 and d=8.
This code was found by Heurico 1.16 in 0.0633 seconds.