The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1  1  1  1  1 12  1 10  1  1  1  1  1  1  1  1  1  1
 0  1  3  6  5  1 12 15  1 10  9  1  6  3  1  1  5  0 12 15  9  0  1  5  1 12 10  6 10 10  0  6  3  9  5
 0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  0  0  8  8  0  0  8  8  8  8  0  8  8  8  8  8  0  8  0
 0  0  0  8  0  0  0  8  0  8  8  8  0  8  8  0  8  0  0  0  8  8  0  8  0  0  0  8  8  0  0  0  8  0  8
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  8  8  8  8  0  0  8  8  8  0  8  0  8  0  0  0  8  8  0  8
 0  0  0  0  0  8  0  8  8  0  8  0  0  0  8  0  8  8  8  8  0  8  8  0  0  8  8  0  8  8  8  8  8  8  0
 0  0  0  0  0  0  8  8  0  8  0  8  8  0  8  0  8  8  8  0  8  0  8  8  8  0  8  0  8  8  0  8  0  8  8

generates a code of length 35 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+16x^29+89x^30+256x^31+399x^32+1328x^33+800x^34+2432x^35+800x^36+1328x^37+383x^38+256x^39+76x^40+16x^41+7x^46+4x^48+1x^54

The gray image is a code over GF(2) with n=280, k=13 and d=116.
This code was found by Heurico 1.16 in 6.17 seconds.