The generator matrix

 1  0  0  0  1  1  1  6  1  1
 0  1  0  0  2  5  7  1 12  4
 0  0  1  0  3  1  2  3 14  0
 0  0  0  1  1  2  3  3  4  2

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

Homogenous weight enumerator: w(x)=1x^0+94x^6+960x^7+3951x^8+14912x^9+25700x^10+14912x^11+3951x^12+960x^13+94x^14+1x^20

The gray image is a code over GF(2) with n=80, k=16 and d=24.
This code was found by Heurico 1.16 in 2.69 seconds.