The generator matrix

 1  0  0  1  1  1 10  2  1  1  1  1 10  4  6  1 12  1  1  1  2  1  1 12  1 10  1  1  0  1  1  6  4 14  1  6  1  1  1
 0  1  0  4  5  1  1  2  5  9  4  8  0  1  1  3  1 15  2  0  1  6 14  1  3  1  9  8 14  4 15 14  6  1  5  1  8  6  8
 0  0  1  7  3  4  3  1  5 10  1 14  1  2  5  6  5  5  2 13  2  5 15  0 10 14  0  7  1 11  4  1  1  3  6  9 12  3  8
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  8  8  0  8  0  8  0  8
 0  0  0  0  8  0  8  8  0  8  0  0  0  8  0  8  0  8  8  8  0  0  8  8  0  8  0  8  0  8  0  8  0  0  0  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+95x^34+656x^35+1460x^36+1922x^37+3015x^38+2376x^39+2948x^40+1808x^41+1174x^42+580x^43+225x^44+70x^45+35x^46+4x^47+5x^48+8x^49+1x^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 1.37 seconds.