The generator matrix

 1  0  1  1  1  6  1  1  0  1 14  1  1  1 14  1  1  8  1  1  6  1 12  1  1  1  1 14  1  1  1 14  1  1  1  8 10  1  1 14  1  1 12 12  1  1  1  8
 0  1 11  6  1  1  8  5  1 10  1  3 11  0  1  5 14  1 13  0  1 15  1  2  8 13  5  1 13  9  3  1  6  8  9  1  1  2  2  1  7  6  1  2  4  0  3  2
 0  0 12  0  0  0  0  0  0  0  0  8  8 12 12  4 12 12  4 12  4 12  4 12  0  4  4  8 12  8  0  8  0 12 12  8  0  4 12 12 12  8  8  4 12 12  8  4
 0  0  0 12  0  0  0  0  4 12 12 12 12 12  8  4  0  4 12  0  8  8  4  4  4  4  0  0  8  4 12 12  4  4  8 12 12  0  4 12  4  0 12  8  0  4 12  0
 0  0  0  0  4  0  8  4  0  8  0  4  4  4 12  8 12 12  8 12 12  0 12  4  4  4  4 12 12  0  8  4 12  0  0 12 12 12  8 12  8  0  0  0  8  8  8  8
 0  0  0  0  0 12 12  4 12  4  8  0  4 12 12  8  4  8  4  0  8 12  4  8  4  8  8  8  4  8 12 12  0  8  0 12  8  8  4  8 12 12  4  0  8  0  4  8

generates a code of length 48 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+72x^39+146x^40+328x^41+496x^42+1164x^43+2622x^44+4490x^45+7416x^46+10276x^47+11493x^48+10434x^49+7410x^50+4528x^51+2494x^52+1090x^53+506x^54+252x^55+118x^56+102x^57+38x^58+28x^59+20x^60+4x^61+6x^62+2x^64

The gray image is a code over GF(2) with n=384, k=16 and d=156.
This code was found by Heurico 1.16 in 36.1 seconds.