The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+74x^39+166x^40+280x^41+736x^42+988x^43+2967x^44+4342x^45+7839x^46+9678x^47+11421x^48+9716x^49+7869x^50+4346x^51+2951x^52+936x^53+651x^54+240x^55+150x^56+84x^57+55x^58+34x^59+6x^60+2x^61+2x^62+1x^64+1x^72

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 92.1 seconds.