The generator matrix

 1  1  1  1  1
 0  2  0  0  8
 0  0  2  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+18x^1+125x^2+504x^3+1666x^4+11756x^5+1666x^6+504x^7+125x^8+18x^9+1x^10

The gray image is a code over GF(2) with n=40, k=14 and d=4.
This code was found by Heurico 1.16 in 0.0124 seconds.