The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  1  1  1  2 12  1  1  1  1  1  2  1  1  1  0  1  1  2  2 12  1  0  1  1 12  2  2  1  1  1  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  4 10  0  8  6 14  6  2 10 12 12  6  0 10  2  0 10 10 12  6  6  8  4 10  2  0  8 10  6  2  8  2  2 12  2 10  6 10  0  0 12  0
 0  0  8  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  8  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  8  8  0  8  8  8  8  0  0  0  8  0  0  0  0  8  8  8  0
 0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  0  0  8  8  0  0  8  8  0  8  0  0  8  8  0  8  0  8  8  8  0  8  8  8  8  0  0  0  0  0  8  8  8  8  8  0  8  0
 0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  0  0  0  0  8  8  8  0  0  8  8  0  8  8  0  0  8  8  0  8  0  8  0  8  8  8  8  0  8  8  0  0  8  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  0  8  0  0  0  8  0  8  0  0  8  8  0  0  0  8  8  0  0  8
 0  0  0  0  0  0  8  0  8  0  8  8  0  8  0  8  8  8  8  0  8  0  8  0  8  8  0  8  8  8  8  8  0  0  0  8  0  8  8  8  8  8  8  8  8  0  8  0  0  8  8  8  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  0  0  0  8  0  8  0  8  0  8  8  0  8  8  0  8  0  8  0  0  8  8  8  0  0  8  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+63x^46+26x^47+147x^48+126x^49+409x^50+650x^51+761x^52+1502x^53+869x^54+1502x^55+743x^56+650x^57+389x^58+126x^59+120x^60+26x^61+49x^62+12x^64+8x^66+5x^68+3x^70+1x^72+1x^74+2x^76+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 1.25 seconds.