The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  8  6 14  0  1  1  1  1  2  2 12  1  1 10  1  1  1  8  1 14 14  1  1  1  1  1  4  1
 0  1  0  0  5 11  1  6  9  1  8  8  0  1  1 15 12 13  2  1  1  6 12  1  1 11  2  2  1  6  6  1  8 15  6 13  6  1 14
 0  0  1  1  1  4  1  9 10 11  6  1  1  2  1 10  4 11 15  5  2  1  9  2  8 13  1  6  3  2  1  2  4  6 11  0  2 10  1
 0  0  0  2 10  8 10  2  4 14 12  6  6  6 12 10 14  0  0  4  8  6  0  2 12  6  0  4  4  0  8 10  2  6  4 10 12  4 14

generates a code of length 39 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+510x^34+1200x^35+2511x^36+4248x^37+5088x^38+5660x^39+5462x^40+4080x^41+2286x^42+1032x^43+420x^44+152x^45+84x^46+12x^47+21x^48+1x^52

The gray image is a code over GF(2) with n=312, k=15 and d=136.
This code was found by Heurico 1.16 in 246 seconds.