The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+213x^46+296x^47+719x^48+868x^49+1787x^50+2156x^51+3635x^52+4256x^53+4783x^54+4460x^55+3695x^56+2296x^57+1696x^58+740x^59+558x^60+256x^61+193x^62+28x^63+80x^64+4x^65+29x^66+15x^68+3x^70+1x^72

The gray image is a code over GF(2) with n=432, k=15 and d=184.
This code was found by Heurico 1.16 in 51.4 seconds.