The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+558x^51+828x^52+658x^53+543x^54+510x^55+322x^56+282x^57+158x^58+108x^59+64x^60+52x^61+1x^62+8x^63+1x^64+2x^70

The gray image is a code over GF(2) with n=432, k=12 and d=204.
This code was found by Heurico 1.16 in 23.9 seconds.