The generator matrix

 1  1  1  1  1  1  1  1  2  2  2  2  0  0  0
 0  2  0  2  0  0  2  2  0  2  2  0  2  2  0
 0  0  2  2  0  2  2  0  2  2  0  0  0  2  2

generates a code of length 15 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+15x^16

The gray image is a code over GF(2) with n=30, k=4 and d=16.
This code was found by Heurico 1.16 in 0.000469 seconds.