The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+141x^46+100x^47+323x^48+612x^49+615x^50+1536x^51+1258x^52+2844x^53+1670x^54+2912x^55+1096x^56+1564x^57+556x^58+560x^59+256x^60+100x^61+123x^62+12x^63+66x^64+29x^66+6x^68+2x^70+2x^72

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 5.1 seconds.