The generator matrix

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

generates a code of length 5 over Z16 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+10x^1+45x^2+120x^3+210x^4+3324x^5+210x^6+120x^7+45x^8+10x^9+1x^10

The gray image is a code over GF(2) with n=40, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00133 seconds.