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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+126x^40+399x^42+56x^43+551x^44+344x^45+1373x^46+1464x^47+2687x^48+2392x^49+2737x^50+1512x^51+1334x^52+328x^53+532x^54+40x^55+285x^56+8x^57+135x^58+67x^60+7x^62+4x^64+1x^66+1x^72

The gray image is a code over GF(2) with n=392, k=14 and d=160.
This code was found by Heurico 1.16 in 5.15 seconds.