The generator matrix

 1  0  0  1  1  1 10  4  2  0  1  1  1  1  6 10  1  1  8  1  1 12  1  2 14  1  4  1  1  6  6  1 14  0  1  1  1  6  1  1  1  4  1  1  1  1  1 12 12  2 14  1  1  1
 0  1  0  4  5  1  1  1  1  6  0  8 15  1  6  1  2  7  1  6  5  1  6  1  4 15  1  9  9  1  1  2  2  6  7 12  6  1 15 13  8  1 14 11 15  8  8  1  0  1  0  4 13  0
 0  0  1  7  3  4  3  2  1  1  6  1  3  2  1  6  1  2  7  6  5  5  0  4  1  5  4  6  0  9  0  7  1  1  7  6 14  6  4  4  7  1 15 15  9  6 12  5  1  2  1  9 15  0
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  8  0  0  0  8  0  0  8  8  8  8  0  8  0  0  8  0  0  8  0  8  8  8  0  8  8  8  8  8  0  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  0  8  8  8  0  8  0  8  8  8  0  8  0  8  0  8  8  8  8  8  0  0  8  8  8  0  8  8  8  0  8  8  0  0  0  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  0  8  0  8  8  8  8  0  0  0  0  0  0  0  8  0  0  8  0  8  8  0  8  8  8  0  0  8  0  8  0  0  0  8  8  8  8  8  0
 0  0  0  0  0  0  8  8  0  8  0  0  8  8  8  0  0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  0  0  8  0  0  8  0  8  0  8  0  8  8  8  8  0  8  8  8  0  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+38x^46+210x^47+1006x^48+1450x^49+3382x^50+4764x^51+8216x^52+8176x^53+11119x^54+8398x^55+8268x^56+4472x^57+3271x^58+1418x^59+913x^60+220x^61+95x^62+56x^63+22x^64+14x^65+15x^66+2x^67+3x^68+4x^69+3x^72

The gray image is a code over GF(2) with n=432, k=16 and d=184.
This code was found by Heurico 1.16 in 30.4 seconds.