The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+104x^49+304x^50+254x^51+648x^52+394x^53+879x^54+360x^55+551x^56+170x^57+234x^58+78x^59+35x^60+24x^61+31x^62+12x^63+4x^64+10x^65+2x^69+1x^84

The gray image is a code over GF(2) with n=432, k=12 and d=196.
This code was found by Heurico 1.16 in 0.4 seconds.