The generator matrix

 1  0  0  1  1  1  2  4  1  1  0 14  1  1  1  1  8  2  4  1  2  1  1  2  1  1  1  1 10  1  4  1 12  1  8  1  0  1 14  1  1 12  6  1  6  1  1 14  1  8  4  1  1  1
 0  1  0  2  1 11  1  6 14  9  1  1 15  6 11  0  1  4  1 10  1 11  0 14 13  6  9  7  1  1 14  7  1  1  4  4  1  2  2  4  7  1  1  7  1 11  4  1 12  1  1 15  8  0
 0  0  1  1  3  4  5  1  6  2  9  0  5  3  2  9  6  1  7 12  2 13 11  1 13 13  0  0 13  5  1 14 10  3  1  9  4 14  1  4  8  3  2 15  9  0 10 15  1  7  5 15  3  0
 0  0  0  4  0  0 12 12  4 12  8  4 12 12  4  8 12  4 12  4  8  4  4  0 12  0  8  8  0  0  8  0  8  8  4  8 12  0  8  4  4  0 12 12  4  8  8 12  0  0  0 12 12  0
 0  0  0  0  4  8  8  8  8  0  0  0  4  4  4  4  4  4 12 12 12  8 12 12  4  0  8 12  4  8  4  0  4  0  0  8  8  4  0 12  0  8  0  0 12  0  0  8  4 12 12 12  0  0

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

Homogenous weight enumerator: w(x)=1x^0+46x^46+208x^47+741x^48+2014x^49+2987x^50+5334x^51+6968x^52+9940x^53+9252x^54+9692x^55+7028x^56+5744x^57+2966x^58+1444x^59+558x^60+358x^61+134x^62+54x^63+30x^64+22x^65+7x^66+2x^67+2x^68+2x^69+2x^71

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 30.9 seconds.