The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+56x^28+172x^29+490x^30+1178x^31+2050x^32+4052x^33+5111x^34+6642x^35+5030x^36+4056x^37+2130x^38+1106x^39+404x^40+164x^41+64x^42+30x^43+10x^44+4x^45+12x^46+4x^47+1x^48+1x^50

The gray image is a code over GF(2) with n=280, k=15 and d=112.
This code was found by Heurico 1.16 in 5.48 seconds.