The generator matrix

 1  0  1  1  1 14  1  1  0 14  1  1  1  0  1  2  1  1  1  8  1  1  1  8  1  6  1 10  1  1  1  1 12  1  1  0 14  1  1  1  1  2  1 12  1  1  0  1  1  2  1  1  8  1
 0  1 11  6  1  1  8  3  1  1 14  9  6  1  3  1 13  0  3  1  8 10  9  1 15  1 14  1 12 13 11  6  1 10 11  1  1 11  9  2  8  1  4  2 14  1  1  4  7 14  6  4  4  4
 0  0 12  0  0  0  0  8 12  4  4  4 12 12  0  4  8  8 12  8  4  4  4  0  0  4  0  8  4 12  0  8  0 12 12 12  8  4  8 12  0  8  0  0  4  8  4  4 12  0  8  4  4  4
 0  0  0 12  0  0  8  8  8  8  0  8  8 12 12 12 12 12 12 12 12 12  4  4  4  8  0  0 12  0  4  4 12  0 12  4 12  4  0 12  8  4 12  8 12 12  8  8  4 12  8  8 12  4
 0  0  0  0  4 12 12  8  4  0  0  4  4  8 12  4  0  4 12  4 12  8  0  0  4 12 12  0  8  8  0 12  4 12  8  8 12 12  8  4  8  0  8  4 12 12  4  8  8 12  8  0 12 12

generates a code of length 54 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+52x^47+210x^48+466x^49+761x^50+1308x^51+1942x^52+2260x^53+2428x^54+2394x^55+1897x^56+1218x^57+767x^58+382x^59+120x^60+74x^61+37x^62+18x^63+11x^64+12x^65+4x^66+6x^67+10x^68+2x^69+3x^70+1x^72

The gray image is a code over GF(2) with n=432, k=14 and d=188.
This code was found by Heurico 1.16 in 2.92 seconds.