The generator matrix

 1  0  0  0  1  1  1  1
 0  1  0  0  2  5  7  0
 0  0  1  0  3  1  2  0
 0  0  0  1  1  2  3  0

generates a code of length 8 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+186x^4+992x^5+4072x^6+12704x^7+29626x^8+12704x^9+4072x^10+992x^11+186x^12+1x^16

The gray image is a code over GF(2) with n=64, k=16 and d=16.
This code was found by Heurico 1.16 in 0.523 seconds.