The generator matrix

 1  0  1  1  4  1 10  1  1  1  1  6 10  1  1  1  1  4  1  1  8  1  1 10  0  1  4  1  1  1  2  8  1  1  1
 0  1  1  6  1  7  1  4 15  2  5  1  1  8  3 14 13  1 10 11  1  4  9  1  2  8  1 14  3 14  0  1  3 11  8
 0  0  2  0 10  2  6 10  8 10  8  0 10 14  6 14  6  6  0  4 12  4  8  0  6 12  4  4 14  6  6 10  4  0 12
 0  0  0  8  0  8  8  8  8  0  0  8  8  8  8  0  0  0  0  0  8  8  8  0  8  0  0  8  0  8  0  8  8  0  8

generates a code of length 35 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+98x^31+324x^32+628x^33+643x^34+936x^35+495x^36+492x^37+267x^38+126x^39+43x^40+16x^41+17x^42+8x^43+1x^44+1x^46

The gray image is a code over GF(2) with n=280, k=12 and d=124.
This code was found by Heurico 1.16 in 0.115 seconds.