The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+246x^34+624x^35+1210x^36+2092x^37+2592x^38+3084x^39+2485x^40+2054x^41+1104x^42+520x^43+213x^44+56x^45+72x^46+12x^47+10x^48+6x^49+2x^50+1x^52

The gray image is a code over GF(2) with n=312, k=14 and d=136.
This code was found by Heurico 1.16 in 2.06 seconds.