The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^48+234x^49+346x^50+802x^51+937x^52+1304x^53+1008x^54+1254x^55+865x^56+780x^57+293x^58+210x^59+65x^60+10x^61+11x^62+4x^63+2x^64+6x^65+4x^66+6x^68+2x^69+2x^71+1x^74+1x^78

The gray image is a code over GF(2) with n=432, k=13 and d=192.
This code was found by Heurico 1.16 in 0.775 seconds.