The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+145x^24+8x^26+375x^28+176x^30+750x^32+448x^34+12288x^35+950x^36+336x^38+595x^40+56x^42+200x^44+45x^48+10x^52+1x^60

The gray image is a code over GF(2) with n=280, k=14 and d=96.
This code was found by Heurico 1.16 in 3.07 seconds.