The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2 12  1  1  1  1  2  2  0  1 12  1  1  1  2  1  1  0  1  1  1  1  2  2  2  0  2  2  1  1  2  2  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  0  6  6  2 12 10 10  2  6  0 12 10  6 10  2  6  2 10  6  0  6 10  6  2 12 10  0  6 10  6 10  2 10  6 12  0  6  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  8  0  0  8  0  8  8  0  8  8  8  8  8  8  8  0  0  0  8  0  0  8  0  0  0  8  8  0  8  0  8  8  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  8  8  0  8  8  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  8  0  8  0  8  8  0  8  0  8  0  0  0  0  8  8  0  8  0  8  8  8  0  8  0  8  8  0  0  0  0  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  8  8  0  0  8  8  8  0  0  0  8  0  8  0  8  8  0  8  8  8  0  8  8  0  8  0  8  0  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  0  8  8  0  0  0  0  8  8  8  0  0  8  8  8  0  8  0  8  0  8  8  8  8  8  0  8  8  0  0  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  8  0  8  0  8  8  8  0  0  0  0  8  8  0  8  8  0  8  0  8  8  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  8  8  8  0  8  8  0  8  0  0  0  0  0  8  0  8  8  0  0  8  8  8  0  0  0  0  0  8  8  8  0  0  0  8  0  0  0
 0  0  0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  8  8  0  0  8  0  8  0  0  8  8  8  0  8  0  0  0  8  8  0  8  8

generates a code of length 52 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+62x^40+4x^41+36x^42+32x^43+318x^44+144x^45+456x^46+644x^47+1876x^48+1688x^49+4912x^50+2608x^51+7309x^52+2608x^53+4824x^54+1688x^55+1848x^56+644x^57+492x^58+144x^59+253x^60+32x^61+32x^62+4x^63+83x^64+23x^68+2x^72+1x^76

The gray image is a code over GF(2) with n=416, k=15 and d=160.
This code was found by Heurico 1.16 in 15.5 seconds.