The generator matrix

 1  0  0  1  1  1  6  1  1
 0  1  0  1  6  7  1  0  4
 0  0  1  1  3  2  3  6  4
 0  0  0  8  0  0  8  8  0

generates a code of length 9 over Z16 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+79x^6+584x^7+1461x^8+3952x^9+1450x^10+584x^11+74x^12+7x^14

The gray image is a code over GF(2) with n=72, k=13 and d=24.
This code was found by Heurico 1.16 in 0.047 seconds.