The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  1  0  1  1 14  1  1  1  4  1  1  4  1 10  1  0  1  1  1  1 14 14  1  1 12  1 14  1  1  4 12 10  1 10  2  1  1
 0  1 11  6  1  1  0 11  1  6  1 13  0  1  3  5  1  4 15  6  1 13  2  1  7  1 14  1  3  0  6  1  1  1  7  2  1  2  1  8  3  0  1  1  1  1  1  6  0
 0  0 12  0  0  0  0  0  0  8  8  4  4  4  8 12  4  4  4 12  4  8  0  0  4 12  0  4 12 12  4  4  4 12  8  8  0  4  8 12  8 12  4 12  0  8 12 12  0
 0  0  0 12  0  0 12  8  4  8 12  0  0  0 12 12 12  4  4  0 12  8 12 12  8  0  4 12  8 12 12  4  8  0 12  8  4 12  8  0  0  4  8  4 12  8 12  0  0
 0  0  0  0  4  0  0 12  8  0  8  0  4 12  4  8 12  4  0  4 12 12  0  8  8  4  8  0  4  0  8  4  8  8  0  4 12  4  4  8  0  8 12  0  0  8 12 12  0
 0  0  0  0  0  8  0  0  8  0  8  0  0  8  0  0  8  0  0  8  0  8  8  0  8  8  8  8  0  0  8  8  8  8  8  0  0  8  0  0  0  0  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  8  0  8  8  8  0  8  8  0  8  0  8  0  0  0  8  8  8  0  0  8  8  8  8  8  0  8  8  8  8  0  0  0  8  0  8  8  0  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+133x^40+32x^41+472x^42+368x^43+1582x^44+2260x^45+4998x^46+7192x^47+10205x^48+10916x^49+10370x^50+7400x^51+5026x^52+2140x^53+1338x^54+392x^55+463x^56+12x^57+150x^58+8x^59+54x^60+16x^62+6x^64+2x^68

The gray image is a code over GF(2) with n=392, k=16 and d=160.
This code was found by Heurico 1.16 in 36.7 seconds.