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

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

Homogenous weight enumerator: w(x)=1x^0+48x^41+113x^42+178x^43+211x^44+252x^45+496x^46+862x^47+1229x^48+1454x^49+1230x^50+830x^51+524x^52+246x^53+182x^54+166x^55+72x^56+42x^57+24x^58+8x^59+9x^60+6x^61+2x^62+4x^63+2x^64+1x^74

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 1.29 seconds.