The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2 12  2  2  2  2  2 12  1  1  2  4  2  1  2  8  0  1  1
 0  2  0  0  0  0  0  0  0  2 14 10 14  2 14 14  8  8  6  6  4 12  4  4  2  4  2  2  8  6  6  0  2  2 12
 0  0  2  0  0  8 10  6  6 10 14  8  2 14 12  4  2  2  4 14  0  4 14  4 12  2  8  0 12  0  8  8 14 10 14
 0  0  0  2  0 10 10 10  8  2  6  8 12  0  6  6  2 12  2 10 14  6  0  0 10  0  4 10 12  2 12  2  2 12  6
 0  0  0  0  2  2  8 10  2  6  8 14 10 12  6 12  4 12  0 10  0 14  6  2  0  6 12  8 10 14 10  4 12 14 10

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

Homogenous weight enumerator: w(x)=1x^0+274x^28+684x^29+1584x^30+2572x^31+4596x^32+7498x^33+9799x^34+10702x^35+10870x^36+7682x^37+4444x^38+2484x^39+1433x^40+518x^41+223x^42+94x^43+42x^44+18x^45+14x^46+4x^47

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 30.5 seconds.