The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0  2  0  0  4 14 10 10  0  4
 0  0  2  0  6  6  6  4  8 12
 0  0  0  2  2  4  6  2  4  8

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

Homogenous weight enumerator: w(x)=1x^0+34x^6+208x^7+383x^8+1072x^9+4796x^10+1072x^11+383x^12+208x^13+34x^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 0.0719 seconds.