The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^31+203x^32+448x^33+677x^34+1184x^35+1719x^36+3798x^37+4546x^38+7450x^39+4536x^40+3846x^41+1908x^42+1214x^43+536x^44+338x^45+158x^46+72x^47+42x^48+18x^49+7x^50+10x^51+1x^52+2x^56

The gray image is a code over GF(2) with n=312, k=15 and d=124.
This code was found by Heurico 1.16 in 9.67 seconds.