The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^46+74x^47+125x^48+292x^49+256x^50+436x^51+1296x^52+492x^53+2263x^54+508x^55+1296x^56+420x^57+230x^58+232x^59+68x^60+68x^61+26x^62+26x^63+24x^64+8x^65+9x^66+4x^67+4x^68+3x^70+2x^72+1x^82

The gray image is a code over GF(2) with n=432, k=13 and d=184.
This code was found by Heurico 1.16 in 1.19 seconds.