The generator matrix

 1  0  1  1  6  1  4  1  1  1  1 10  1  8  1  1  1  8 14  1  1  1  1 14 14  4  1  1  1  2  1  1  1  0  1  4  2  1  2  1  1  1  2  1  1  0  1  0  2  2  2  1  2  1
 0  1  1  6  1  7  1  4  3  5  2  1 11  1  8  6 11  1  1  9 12  2  5  1  1  1 10  9  3  1  9  0 14  1  1  1  1  0  8  6  8  8  4  8 13 12  5  1  1 14  1  7  4  8
 0  0  2  0  0  2 10 10  0  8 10  6 10  4 10 14 12 10 10  8  0  4  6  4 12 12  8 14 14 10  8 14  6 14 12  2 12 12 10  8 14  4  2  0 10  2 10 10 14 10  8  6  6  8
 0  0  0  8  0  0  8  0  8  8  0  8  0  0  0  0  8  8  8  8  0  8  0  8  8  0  0  8  8  0  0  8  8  0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  0  8  0  8  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  0  0  8  8  8  8  8  8  8  8  0  8  8  0  8  0  0  0  0  8  0  8  0  8  8  0  0  0  8  8  8  8  0  0  0  0  8  0
 0  0  0  0  0  8  8  0  8  8  0  8  8  8  8  8  0  0  0  0  8  8  0  0  8  8  8  0  8  8  0  0  8  0  8  8  8  0  0  8  0  8  0  8  8  8  8  8  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+159x^48+384x^49+1013x^50+1424x^51+1870x^52+2312x^53+2341x^54+2432x^55+1703x^56+1184x^57+787x^58+352x^59+205x^60+88x^61+75x^62+16x^63+29x^64+4x^66+1x^68+4x^70

The gray image is a code over GF(2) with n=432, k=14 and d=192.
This code was found by Heurico 1.16 in 2.72 seconds.