The generator matrix

 1  1  1  1  2  2  1  1  1  1
 0 12  0 12 12 12  0  0  0  0
 0  0  8  0  0  0  0  0  0  8
 0  0  0  8  0  0  0  0  0  8
 0  0  0  0  8  0  0  0  0  8
 0  0  0  0  0  8  0  0  0  8
 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

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

Homogenous weight enumerator: w(x)=1x^0+53x^4+48x^6+842x^8+6304x^10+842x^12+48x^14+53x^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 0.021 seconds.