The generator matrix

 1  1  1  1  2  1  2  1  1  1
 0  2  0  6  2  0  6 14  8  0
 0  0 12  0  0  0  4  8  8 12
 0  0  0 12  0 12  4  8  0  4
 0  0  0  0  4  0  8 12  4  8
 0  0  0  0  0  8  8  8  8  0

generates a code of length 10 over Z16 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+42x^5+105x^6+292x^7+1028x^8+2734x^9+7967x^10+2744x^11+1044x^12+294x^13+87x^14+36x^15+7x^16+2x^17+1x^18

The gray image is a code over GF(2) with n=80, k=14 and d=20.
This code was found by Heurico 1.16 in 3.04 seconds.