The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^41+59x^42+128x^43+169x^44+356x^45+512x^46+1020x^47+1070x^48+1540x^49+1071x^50+1036x^51+500x^52+364x^53+130x^54+116x^55+38x^56+20x^57+11x^58+4x^59+8x^60+6x^62+3x^64+3x^66+2x^68+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 40.9 seconds.