The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^40+74x^41+161x^42+314x^43+352x^44+798x^45+1287x^46+1402x^47+2762x^48+1950x^49+2852x^50+1566x^51+1286x^52+678x^53+241x^54+270x^55+137x^56+80x^57+55x^58+32x^59+26x^60+4x^61+7x^62+5x^64+4x^66+1x^70

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 4.03 seconds.