The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+36x^46+74x^47+258x^48+194x^49+785x^50+1178x^51+2032x^52+2310x^53+2606x^54+2582x^55+1859x^56+1042x^57+860x^58+254x^59+186x^60+34x^61+47x^62+8x^63+9x^64+4x^65+11x^66+6x^68+6x^70+1x^72+1x^78

The gray image is a code over GF(2) with n=432, k=14 and d=184.
This code was found by Heurico 1.16 in 2.89 seconds.