The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+248x^48+720x^49+2100x^50+2612x^51+3974x^52+4176x^53+5402x^54+4180x^55+4092x^56+2304x^57+1608x^58+748x^59+397x^60+96x^61+66x^62+12x^63+18x^64+8x^66+5x^68+1x^72

The gray image is a code over GF(2) with n=432, k=15 and d=192.
This code was found by Heurico 1.16 in 8.35 seconds.