The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+141x^44+56x^45+226x^46+240x^47+552x^48+1096x^49+882x^50+1824x^51+928x^52+1096x^53+470x^54+240x^55+256x^56+56x^57+86x^58+23x^60+14x^64+4x^68+1x^80

The gray image is a code over GF(2) with n=408, k=13 and d=176.
This code was found by Heurico 1.16 in 1.14 seconds.