The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0  2  0  2  0 12 10 14  0  0
 0  0  2  2  0  2 14  0  0  0
 0  0  0  4 12 12  0  4  0  0
 0  0  0  0  8  0  0  8  0  0
 0  0  0  0  0  8  0  8  0  0
 0  0  0  0  0  0  8  8  0  0

generates a code of length 10 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+93x^4+192x^5+480x^6+960x^7+1314x^8+2944x^9+20800x^10+2944x^11+1314x^12+960x^13+480x^14+192x^15+93x^16+1x^20

The gray image is a code over GF(2) with n=80, k=15 and d=16.
This code was found by Heurico 1.16 in 0.217 seconds.