The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^41+194x^42+268x^43+398x^44+742x^45+1104x^46+1774x^47+2437x^48+2512x^49+2388x^50+1868x^51+1128x^52+644x^53+353x^54+228x^55+106x^56+62x^57+42x^58+16x^59+26x^60+14x^61+14x^62+6x^63+1x^70

The gray image is a code over GF(2) with n=392, k=14 and d=164.
This code was found by Heurico 1.16 in 4.14 seconds.