The generator matrix

 1  0  0  1  1  1  8  0  1  1  8 14  1  1  1 10  1  1  6 12  1  1 10  4  1  8  1  1  1  4  1  1  8  1  2 12 14  8  2  1  1  1  1  1  1  1  1  1
 0  1  0  0  5  3  1 14 15  2  1  1 14  9  5  1 14  8  6  1  1  2  1  4  0  1  7  3 11  1 13  7  1  9  8  6  1  4  1  2  8  4  5  5  7  0 13  0
 0  0  1 11  7  0  3  1  5 14  6  7  7  4  1 10  8  5  1  1 10  5  5  1 10 10  9  7  2  4 12 11  3  7  1  1  8  1  7 10  9  9 14  6  2  5 13  0
 0  0  0 12  4  8 12 12  0 12  4  8  0  4  4  8  4  8  0 12 12 12  0 12  0 12  4  0  4  4  8  4  8  0  4  4  8 12  4  8  0  0  0 12  4  4 12  8
 0  0  0  0  8  0  8  8  0  8  8  0  8  0  0  8  0  0  8  0  8  0  0  8  8  0  0  0  0  8  8  8  8  0  8  0  8  0  0  0  0  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+160x^42+630x^43+1805x^44+2504x^45+4172x^46+4174x^47+5820x^48+4678x^49+4014x^50+2252x^51+1645x^52+484x^53+256x^54+78x^55+33x^56+46x^57+6x^58+2x^59+6x^60+2x^64

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 7.09 seconds.