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

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

Homogenous weight enumerator: w(x)=1x^0+411x^34+1442x^35+2535x^36+3736x^37+5387x^38+5850x^39+5533x^40+3800x^41+2243x^42+1102x^43+453x^44+176x^45+69x^46+22x^47+6x^48+2x^50

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 20.6 seconds.