The generator matrix

 1  0  1  1  1
 0  1  1  0  0
 0  0  2  0  4
 0  0  0  2  4

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

Homogenous weight enumerator: w(x)=1x^0+85x^2+400x^3+2730x^4+9952x^5+2730x^6+400x^7+85x^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 0.0196 seconds.