The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+106x^42+776x^43+1606x^44+2764x^45+3782x^46+4888x^47+5035x^48+5060x^49+3712x^50+2672x^51+1338x^52+614x^53+246x^54+96x^55+28x^56+24x^57+10x^58+8x^60+2x^61

The gray image is a code over GF(2) with n=384, k=15 and d=168.
This code was found by Heurico 1.16 in 7.78 seconds.