The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^42+176x^43+335x^44+912x^45+584x^46+1636x^47+940x^48+1578x^49+583x^50+906x^51+284x^52+134x^53+29x^54+16x^55+5x^56+14x^57+12x^58+2x^59+3x^60+2x^61+5x^62+1x^66

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 0.651 seconds.