The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+66x^41+157x^42+448x^43+569x^44+1512x^45+1369x^46+3164x^47+2000x^48+3004x^49+1394x^50+1556x^51+468x^52+392x^53+132x^54+68x^55+22x^56+18x^57+15x^58+12x^59+11x^60+3x^62+1x^64+2x^66

The gray image is a code over GF(2) with n=384, k=14 and d=164.
This code was found by Heurico 1.16 in 2.51 seconds.