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 12  0  2  4  1  1 12  2  1  4  1 12  0  2  1  2  2  1  1  1  8  2 12  2  1  1  1  4  1  1  1  1
 0  2  0  2  0  8  6 14  0  0  2  6  0  8  6 10  4  2 12 10  2  6  2  2 14  2 14  8  2  2  4  2 10  2  8 12 12  0  4 12 12 14  2  6  2  6 12  4  2  2  0 12  0  6
 0  0  2  2  0  6 14  8  0  2 10  0  4  2  2  4 14 14 12  8 14  4 14 12 12  0  8 14 14  6 10 12 14 10  2  6  4  6  2  0  6 14 14  0  4  2  2  6  2  0 10  2 12  8
 0  0  0  4  0  0 12  0 12 12  8 12 12 12  8  4  4  8  0  8  0  4 12  8  4 12  0 12  0 12  4  0  4  0  4  4 12  8 12 12 12 12  4  4  8  8  8  4  8  8  0  8  4  8
 0  0  0  0 12  4  4  4 12  8  8  4  0 12 12  0  4  4 12 12  0  8 12 12 12  8  8  8  8  0  4  0 12  0 12  8  8  0  0  4  0  0  8 12  8  4 12 12  0 12 12  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+114x^47+364x^48+604x^49+859x^50+1202x^51+1624x^52+2262x^53+2520x^54+2132x^55+1712x^56+1220x^57+765x^58+444x^59+236x^60+158x^61+70x^62+36x^63+27x^64+12x^65+7x^66+6x^67+4x^68+2x^70+2x^71+1x^74

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 4.21 seconds.