The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+144x^31+402x^32+736x^33+1313x^34+2026x^35+3542x^36+5010x^37+6364x^38+5088x^39+3643x^40+2040x^41+1225x^42+650x^43+341x^44+146x^45+55x^46+28x^47+6x^48+4x^49+2x^50+1x^52+1x^54

The gray image is a code over GF(2) with n=304, k=15 and d=124.
This code was found by Heurico 1.16 in 8.94 seconds.