The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+36x^42+118x^43+261x^44+416x^45+607x^46+896x^47+1155x^48+1294x^49+1182x^50+902x^51+593x^52+304x^53+175x^54+116x^55+55x^56+30x^57+10x^58+16x^59+10x^60+4x^61+5x^62+5x^64+1x^70

The gray image is a code over GF(2) with n=392, k=13 and d=168.
This code was found by Heurico 1.16 in 1.03 seconds.