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

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

Homogenous weight enumerator: w(x)=1x^0+40x^41+337x^42+586x^43+921x^44+1488x^45+2254x^46+3644x^47+4669x^48+4946x^49+4763x^50+3562x^51+2261x^52+1558x^53+805x^54+434x^55+286x^56+86x^57+58x^58+28x^59+21x^60+10x^61+5x^62+2x^63+2x^66+1x^68

The gray image is a code over GF(2) with n=392, k=15 and d=164.
This code was found by Heurico 1.16 in 12.5 seconds.