The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+136x^46+60x^47+414x^48+320x^49+813x^50+1176x^51+1391x^52+3056x^53+1735x^54+3040x^55+1421x^56+1184x^57+750x^58+328x^59+287x^60+48x^61+122x^62+4x^63+59x^64+21x^66+9x^68+7x^70+1x^72+1x^76

The gray image is a code over GF(2) with n=432, k=14 and d=184.
This code was found by Heurico 1.16 in 94.3 seconds.