The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+280x^49+1216x^50+1442x^51+1859x^52+2334x^53+2462x^54+2320x^55+1865x^56+1132x^57+767x^58+354x^59+216x^60+60x^61+48x^62+8x^63+8x^64+3x^66+4x^67+3x^68+2x^69

The gray image is a code over GF(2) with n=432, k=14 and d=196.
This code was found by Heurico 1.16 in 2.3 seconds.