The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+44x^31+207x^32+498x^33+789x^34+2316x^35+3753x^36+8372x^37+10130x^38+13428x^39+10085x^40+8388x^41+3732x^42+2232x^43+774x^44+452x^45+190x^46+88x^47+26x^48+18x^49+7x^50+4x^51+1x^52+1x^56

The gray image is a code over GF(2) with n=312, k=16 and d=124.
This code was found by Heurico 1.16 in 24.3 seconds.