The generator matrix

 1  0  0  1  1  1  4 12  1  1  8  1  1 10  8  1  6  1  1 10  1  4  1  6 10  1  1  1  1  1  1  1  1  1  1  1  8  1  1  1 14  1  2  6  0  1  4  1 14  8  1  1  1
 0  1  0  0 13 11  1  1  7  1  1 14 10  8  1 13  0  4  1  1  6  1  3 10  1 12 11 12  9 15  0  2  3  4  9 11  1 15 14  8  1 10  1  1  1 10 14 11  1  1  8 12  0
 0  0  1  1 13  4  7  4  5  0  5  6 15  1  6 11  1  8  4  7  7 15 15  1  6 10 14 11  1  6  4  1 12  1 14  7 14  6  4  9  0  1  0 14  3  5  1 13 15 10  0  9  2
 0  0  0  2 10  0  8 10  4 14  6 10  0 14  0 12  8  6 12  4  6  6  2 14  2  4  4  8  0 14  6  8  6  4 12 14  2  0  8  2  8 10 10  0 12  4 14 14  2 12  4  8 10
 0  0  0  0  8  8  8  8  8  8  8  0  0  0  8  8  0  0  8  0  8  0  0  8  0  8  0  8  0  8  8  8  0  0  0  0  8  0  0  8  0  8  0  8  0  8  0  8  8  8  0  8  0

generates a code of length 53 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+136x^46+656x^47+1645x^48+3320x^49+5147x^50+8034x^51+8460x^52+10452x^53+9259x^54+7976x^55+4943x^56+3102x^57+1308x^58+620x^59+270x^60+128x^61+49x^62+8x^63+9x^64+6x^65+3x^66+2x^67+2x^70

The gray image is a code over GF(2) with n=424, k=16 and d=184.
This code was found by Heurico 1.16 in 30.1 seconds.