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

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

Homogenous weight enumerator: w(x)=1x^0+109x^46+290x^47+758x^48+1254x^49+1824x^50+2348x^51+3392x^52+4300x^53+4269x^54+4296x^55+3491x^56+2552x^57+1666x^58+988x^59+630x^60+260x^61+181x^62+70x^63+45x^64+18x^65+14x^66+8x^67+2x^68+1x^70+1x^72

The gray image is a code over GF(2) with n=432, k=15 and d=184.
This code was found by Heurico 1.16 in 14.5 seconds.