The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+8x^41+48x^42+92x^43+103x^44+308x^45+247x^46+914x^47+626x^48+2776x^49+1055x^50+4112x^51+1062x^52+2720x^53+593x^54+956x^55+205x^56+320x^57+71x^58+68x^59+31x^60+12x^61+21x^62+2x^63+15x^64+9x^66+4x^68+3x^70+1x^72+1x^74

The gray image is a code over GF(2) with n=408, k=14 and d=164.
This code was found by Heurico 1.16 in 85.3 seconds.