The generator matrix

 1  1  1  1  1
 0 12  0  4  0
 0  0 12  4  0
 0  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+15x^2+12x^3+16x^4+424x^5+16x^6+12x^7+15x^8+1x^10

The gray image is a code over GF(2) with n=40, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000133 seconds.