The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^46+162x^47+431x^48+1106x^49+1556x^50+2430x^51+3627x^52+4828x^53+4784x^54+4594x^55+3476x^56+2680x^57+1436x^58+834x^59+368x^60+212x^61+124x^62+36x^63+28x^64+6x^65+8x^66+8x^67+5x^68

The gray image is a code over GF(2) with n=432, k=15 and d=184.
This code was found by Heurico 1.16 in 10.2 seconds.