The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  4  1  1  1  1  4  2  1  2  1  4  1  1  2  2  2
 0 12  0  0  0  0  0  0  0  0  4 12 12  8  4  4  8  4  0  4  0  4  8  4  8  4 12 12  0  4  8 12  4  8 12 12 12  4 12  4  8  0  4 12  8  0  0 12 12  4 12  8  8  8
 0  0 12  0  0  0  4 12 12  8  4  4  8  4  4  0  8 12  8  4  0  8  8 12  4  8  8  8  4  8  4 12 12  4  0  8  0  8  0  4  0  0  0  0  4 12  8 12  8 12  0  8 12  4
 0  0  0 12  0  4  4  4  0  8  0  0  0  0  4 12  4  8  0  8 12  4  8 12  4  4  0 12  4  0  8  4 12  8  4  4 12  4 12  4  0  8  0  8  0  4  4  8  8  4 12  8  4  4
 0  0  0  0 12  4  8  4  4  0  8  4 12 12  4  8  8  4 12  0  4 12  4 12  0  4  8  8  4 12  8  8  8  8 12  4 12 12  4  4 12  8  4  0  8  0  8  0  8  0 12  4  8 12
 0  0  0  0  0  8  8  0  8  8  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  0  8  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  8  8  8  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+122x^46+8x^47+284x^48+36x^49+398x^50+284x^51+786x^52+1224x^53+2016x^54+1184x^55+779x^56+276x^57+316x^58+60x^59+245x^60+112x^62+38x^64+10x^66+8x^68+2x^70+2x^72+1x^84

The gray image is a code over GF(2) with n=432, k=13 and d=184.
This code was found by Heurico 1.16 in 1.45 seconds.