The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+182x^31+708x^32+1306x^33+1094x^34+1816x^35+1147x^36+1010x^37+548x^38+242x^39+75x^40+34x^41+6x^42+16x^43+5x^44+2x^45

The gray image is a code over GF(2) with n=280, k=13 and d=124.
This code was found by Heurico 1.16 in 0.308 seconds.