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  1  1  1  1  1  1  1  1  2  2  2  2  4  1  2  1  4  4  1  1  1  1  4  4  4
 0 12  0  0  0  0  0  0  0  0  4 12 12  8  4  4  8  4  0  4  0  4  8  4  8  4 12 12  0  4  8 12  4  8 12 12 12  4 12  4  0  8  8 12  4 12  8  4  8  4 12
 0  0 12  0  0  0  4 12 12  8  4  4  8  4  4  0  8 12  8  4  0  8  8 12  4  8  8  8  4  8  4 12 12  4  0  8  0  8  0  4  4  0  0  0 12  0  8 12  8 12  0
 0  0  0 12  0  4  4  4  0  8  0  0  0  0  4 12  4  8  0  8 12  4  8 12  4  4  0 12  4  0  8  4 12  8  4  4 12  4 12  4  8  4  8  0  0 12  4  8  0  8  8
 0  0  0  0 12  4  8  4  4  0  8  4 12 12  4  8  8  4 12  0  4 12  4 12  0  4  8  8  4 12  8  8  8  8 12  4 12 12  4  4 12  8 12  8  4  4 12  0 12  8  8
 0  0  0  0  0  8  8  0  8  8  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  0  8  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  0  0  8  0  8  0  8  8  8

generates a code of length 51 over Z16 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+60x^43+117x^44+176x^45+191x^46+270x^47+533x^48+868x^49+1221x^50+1376x^51+1216x^52+862x^53+509x^54+274x^55+180x^56+126x^57+91x^58+58x^59+31x^60+10x^61+4x^62+8x^63+1x^64+6x^65+2x^67+1x^80

The gray image is a code over GF(2) with n=408, k=13 and d=172.
This code was found by Heurico 1.16 in 1.35 seconds.