The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^42+256x^43+523x^44+690x^45+876x^46+1032x^47+1445x^48+1178x^49+870x^50+536x^51+287x^52+198x^53+111x^54+56x^55+56x^56+14x^57+12x^58+8x^59+1x^70

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 0.792 seconds.