The generator matrix

 1  1  1  1  2  1  1  1  1  4
 0  2 12  6  6  0  6 12 10 12
 0  0  8  0  0  8  0  8  8  8
 0  0  0  8  0  8  8  8  0  0
 0  0  0  0  8  8  8  0  0  8

generates a code of length 10 over Z16 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+20x^7+130x^8+96x^9+512x^10+136x^11+120x^12+4x^15+5x^16

The gray image is a code over GF(2) with n=80, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0175 seconds.