The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  8  2  2  2  2  2  0  1  1  1 12  4  2  1  0  0  1
 0  2  0  0  0  2  6 14 12 10  0 14  4 10  8  2  0 14 12  2  8 12  2  6  4  2 14  8  0  4  0  2  0  4  0 10  4  2  0
 0  0  2  0  2  2  2  0  8  2 10 14  4  8 10  4  4  8 14 10  6  4  8 14 10  8  2  2  4  6  4  2  2  2  4  0  2 12  4
 0  0  0  2  2  0  2  2 14  4 14 10  0  2  4  4 12  8  8  2 12  2  2  6 10  4  0  8  2  4  6  6 14  2  2  0  6 12  2
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  8  0  8  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  0  0  8  0  0  8  0  8  8  8  0  0  8
 0  0  0  0  0  0  8  8  8  0  8  0  8  0  8  8  0  0  8  0  8  0  8  8  8  0  8  0  8  8  0  8  8  0  8  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+100x^31+386x^32+960x^33+1230x^34+2952x^35+4054x^36+7862x^37+9206x^38+12038x^39+9056x^40+8016x^41+4236x^42+2930x^43+1178x^44+800x^45+289x^46+150x^47+45x^48+24x^49+14x^50+6x^51+2x^53+1x^62

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 34.5 seconds.