The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^28+314x^29+690x^30+2200x^31+4484x^32+7870x^33+10333x^34+13584x^35+10440x^36+7866x^37+4488x^38+2104x^39+602x^40+330x^41+98x^42+32x^43+12x^44+4x^45+6x^46+1x^48+1x^50

The gray image is a code over GF(2) with n=280, k=16 and d=112.
This code was found by Heurico 1.16 in 16.7 seconds.