The generator matrix

 1  0  1  1  1
 0  1  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+22x^1+141x^2+456x^3+1650x^4+11844x^5+1650x^6+456x^7+141x^8+22x^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 0.0123 seconds.