The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+137x^34+232x^35+622x^36+1032x^37+1326x^38+1584x^39+1308x^40+1008x^41+554x^42+232x^43+100x^44+8x^45+22x^46+7x^48+9x^50+10x^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 0.869 seconds.