The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^34+358x^35+639x^36+1102x^37+1435x^38+1254x^39+1311x^40+1022x^41+533x^42+306x^43+102x^44+34x^45+21x^46+18x^47+2x^48+2x^49+3x^50+1x^52

The gray image is a code over GF(2) with n=312, k=13 and d=136.
This code was found by Heurico 1.16 in 0.517 seconds.