The generator matrix

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

generates a code of length 15 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+66x^4+507x^8+1144x^12+2048x^14+24576x^15+3335x^16+858x^20+221x^24+12x^28

The gray image is a code over GF(2) with n=120, k=15 and d=16.
This code was found by Heurico 1.16 in 0.433 seconds.