The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1  1  1 12  1 10  1  0  6  1  6  1  2  0  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  6  5  1 12 15 10  9  1  5  1  0  1  1  3  1  0  0  1  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  0  0  0  8  0  8  8  8  0  8  8  8  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  0  8  8  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  8  0  8  0  0  8  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  8  8  0  0  8  0  8  0  0  8  8  8  0  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  8  0  8  8  0  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  0  8  0  0  0  8  8  8  0  0  8  8  0  0  8  8  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  0  8  8  0  0  8  0  0  0  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  0  0  0  8  0  8  0  8  0  0  8  0  8  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+82x^24+54x^26+532x^28+64x^29+1230x^30+896x^31+4256x^32+9152x^33+8108x^34+16640x^35+8362x^36+9152x^37+4076x^38+896x^39+1413x^40+64x^41+350x^42+160x^44+6x^46+39x^48+2x^52+1x^56

The gray image is a code over GF(2) with n=280, k=16 and d=96.
This code was found by Heurico 1.16 in 17.1 seconds.