The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  8  1  0  4  1  2  1  2  1  1  1  1  1  0  1  2  0  1  1  1  1  2 12  1  2  1  2  0  1  4  1
 0  2  0  2  0  8  2 10  8  2 12 14  0 10  4  6  8  4  2 14 14 10 10  2  4  0  2  6  0 12  2  6 10 12 12 12 12 14 10  2 12 10  4  6  4  2  2  4  0  2  4  8  2  6
 0  0  2  2 12 14  6 12  0  2 10 12  4 14 14  8  0 10 10  0  4 14  4 12 10  2  6 14  2  4  2 14  0  8  4  2  2  0  4  0  8  0  4  8 10 12  2  6  2 14  2 14  2  6
 0  0  0  4  0  0 12  8  4  8 12 12 12  8  4 12  4 12 12  0  0  0  4  8  8  8 12  0  4 12  8  8 12  4  8  8  0  4  4  8  0  0  4  8  4 12  0  8  8  8 12  4  0 12
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  0  8  8  8  8  0  0  8  0  0  8  0  0  0  8  8  8  8  0  0  8  8  0  0  8  8  8  0  0  8  0  0  0  0  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+145x^48+272x^49+469x^50+704x^51+818x^52+1308x^53+1060x^54+1142x^55+775x^56+618x^57+373x^58+222x^59+134x^60+56x^61+45x^62+26x^63+13x^64+2x^65+4x^66+2x^67+2x^68+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 1.11 seconds.