The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  1  1  2  1  2  1  4  1  1  2  2  1  1  4  8  1  1  4  2
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  8  8  0  0 12  4  0  4  4  0  0  4 12  8  4  0  4  4  0  8 12 12  4  0 12  8 12  4  4 12  4  0
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  0  8 12 12 12  0  0  4 12  8 12  8  4  0  0  4  8  0  4  4 12  0 12  0 12 12 12  8  4  4 12 12
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8  4  0  0  4 12  8  0  4  0  8  0 12  8 12 12  4  0 12  4  0  8  8  8 12  8  8 12  4  0  4  0  8
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  0  8  0  8  8  8  0  0  0  8  8  8  0  8  8  8  8  0  8  8  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  0  0  0  0  8  0  8  0  0  8  0  0  0  8  0  0  0  0  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  8  0  8  0  8  0  8  0  8  8  8  0  0  8  0  0  8  8  8  8  0  0  8  0  8  8

generates a code of length 49 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+74x^41+91x^42+148x^43+177x^44+234x^45+389x^46+902x^47+1409x^48+1412x^49+1426x^50+866x^51+355x^52+268x^53+117x^54+110x^55+89x^56+50x^57+22x^58+18x^59+15x^60+10x^61+2x^62+4x^63+1x^64+1x^66+1x^76

The gray image is a code over GF(2) with n=392, k=13 and d=164.
This code was found by Heurico 1.16 in 1.56 seconds.