The generator matrix

 1  0  1  1  1  4  2  8  1  1
 0  1  1  0  3  1 14  0 10  0
 0  0  2  0  2  4  2  2  4  8
 0  0  0  2  2  6  6  4  2  8

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

Homogenous weight enumerator: w(x)=1x^0+60x^6+320x^7+1111x^8+3904x^9+5592x^10+3904x^11+1111x^12+320x^13+60x^14+1x^20

The gray image is a code over GF(2) with n=80, k=14 and d=24.
This code was found by Heurico 1.16 in 0.167 seconds.