The generator matrix

 1  0  1  1  6  1  1  1  6  1 12  1  8  1  1 12  1  1  1  1 10  1  6  1  4  1 14  0  1  2  1  0 12  4  1  2  1 12  1
 0  1  1  6  1  3  5  4  1  2  1  7  1  8  3  1  1  8  5 11  1 12  1 10  1 10  1  2  0  1  9  1  1  2  7  2  5  1  8
 0  0  2  0  0  8  8 10  6  2  6  2 12 10 12 10  4 12 14 10  0 14  6  8 12  6 12  6  4  2  4  0  4 14  0 14 10  0  4
 0  0  0  8  0  8  0  0  8  0  0  8  8  8  8  8  0  8  8  0  0  8  0  8  0  8  8  8  0  8  8  8  8  0  8  8  0  8  8
 0  0  0  0  8  0  8  0  0  8  0  0  8  8  0  8  0  8  8  8  0  0  8  8  8  0  8  8  0  8  8  0  0  0  8  8  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+94x^34+294x^35+621x^36+1192x^37+1304x^38+1526x^39+1103x^40+988x^41+536x^42+282x^43+159x^44+56x^45+16x^46+10x^47+4x^48+4x^49+2x^50

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 0.454 seconds.