The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+91x^42+474x^43+726x^44+1496x^45+1766x^46+2418x^47+2493x^48+2476x^49+1897x^50+1350x^51+564x^52+360x^53+105x^54+110x^55+20x^56+20x^57+12x^58+2x^60+1x^62+2x^64

The gray image is a code over GF(2) with n=384, k=14 and d=168.
This code was found by Heurico 1.16 in 2.27 seconds.