The generator matrix

 1  0  1  1  1 14  1  1  8  1
 0  1 11  6  5  1  5  0  1  8
 0  0 12  0  0  8  4 12  4  0
 0  0  0 12  0 12  4  4  8  4
 0  0  0  0  8  0  0  8  8  0

generates a code of length 10 over Z16 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+28x^6+96x^7+439x^8+1952x^9+3160x^10+1952x^11+439x^12+96x^13+28x^14+1x^20

The gray image is a code over GF(2) with n=80, k=13 and d=24.
This code was found by Heurico 1.16 in 0.0311 seconds.