The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+88x^27+224x^28+416x^29+708x^30+1832x^31+4134x^32+7650x^33+11359x^34+12776x^35+11296x^36+7726x^37+4074x^38+1788x^39+772x^40+382x^41+145x^42+88x^43+52x^44+18x^45+1x^46+4x^47+1x^48+1x^54

The gray image is a code over GF(2) with n=280, k=16 and d=108.
This code was found by Heurico 1.16 in 62.9 seconds.