The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0 12  0  0  8 12 12  4  0  0
 0  0 12  0 12 12  4  8  0  0
 0  0  0 12  4  8  4  4  0  0

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

Homogenous weight enumerator: w(x)=1x^0+42x^6+63x^8+812x^10+63x^12+42x^14+1x^20

The gray image is a code over GF(2) with n=80, k=10 and d=24.
This code was found by Heurico 1.16 in 0.0025 seconds.