The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+108x^42+268x^43+492x^44+668x^45+872x^46+1148x^47+1192x^48+1152x^49+936x^50+568x^51+310x^52+220x^53+120x^54+60x^55+46x^56+8x^57+12x^58+4x^59+6x^60+1x^64

The gray image is a code over GF(2) with n=384, k=13 and d=168.
This code was found by Heurico 1.16 in 0.902 seconds.