The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+134x^34+212x^35+602x^36+1168x^37+1211x^38+1592x^39+1201x^40+1168x^41+553x^42+212x^43+97x^44+13x^46+14x^48+9x^50+5x^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 0.547 seconds.