The generator matrix

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

generates a code of length 10 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+77x^4+224x^6+434x^8+6720x^10+434x^12+224x^14+77x^16+1x^20

The gray image is a code over GF(2) with n=80, k=13 and d=16.
This code was found by Heurico 1.16 in 0.0188 seconds.