The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 14  2  1  1  1  0  1  1  1  8  1  6  1 14  4  1  1  1  1  1  1  1  1 10  4  2  1  2  1  0  1  8  1  0  1  1  1 12  1  1  1  8  8
 0  1 11  6 13  1  0  7  1 14  5  1  1  6  3  4  1 13  2 13  1 12  1  3  1  1 14  9  9 15 10  7 12  8  1  1  1 13  1  8  1  7  2 13  1 10  7 14  2  4  9  8  2  1
 0  0 12  0  4  0  0  4  0  4  0  4 12  0  8  8  4  8  0  4  8 12  4  4  8 12  0  8  4  4 12  8  8 12 12  8 12 12  0 12  4 12  4  4  0  0  0  8  4  4  0  0  0  0
 0  0  0 12  0  0 12  8  0  8  8  0  0  8  8  4  4 12 12 12 12 12  4  4  4  8 12  8 12 12 12  4  0  8  4 12  0  8 12  0  4  0  8  0  0  0  4 12  0  0  8 12 12  4
 0  0  0  0  8  0  0  8  8  8  0  8  0  8  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  0  0  8  0  0  0  0  8  0  8  8  8  0  8  0  8  0  8  0  8  0  0  0  0  0
 0  0  0  0  0  8  0  8  0  0  8  8  8  0  0  0  0  8  8  0  0  8  0  8  0  0  8  8  0  8  8  8  0  8  0  0  8  0  8  8  8  8  8  8  8  8  8  8  0  0  0  8  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  8  8  8  0  8  8  8  0  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+138x^46+68x^47+508x^48+588x^49+1480x^50+2380x^51+3994x^52+4708x^53+5348x^54+4620x^55+3782x^56+2292x^57+1554x^58+596x^59+404x^60+92x^61+96x^62+16x^63+67x^64+22x^66+10x^68+2x^70+2x^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 11.3 seconds.