The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1  0  1  1  6  2  2  0  2  1  1 10  1  1 12  1
 0  1  3  6  5  1 15 12  1 10  9  1  0  3  1  6  5  1  0  3  1  6  5  1  0  6  2  8 12 11  1 12 15  1  3
 0  0  8  0  0  0  0  8  8  8  8  8  0  0  0  0  0  8  8  8  8  8  8  0  0  0  8  8  0  0  0  8  8  0  0
 0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  0  8  8  0  0  0  8  8  8  8  0
 0  0  0  0  8  0  8  8  8  8  0  8  0  8  0  0  8  8  8  0  8  8  0  0  8  8  0  0  8  0  8  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+80x^31+169x^32+200x^33+484x^34+224x^35+456x^36+184x^37+152x^38+64x^39+14x^40+16x^41+3x^42+1x^58

The gray image is a code over GF(2) with n=280, k=11 and d=124.
This code was found by Heurico 1.16 in 0.0395 seconds.