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  2  1  1  2  2  4  2  1  1  1  2  2  1  1  2  2  1  4  1  0  2  2  4  0  1
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  8  8  0  0 12  4  0  4  4  4  0 12  8  0 12  0 12  4  8  0 12  8  4  8 12  4  0  0  8  0 12 12  4  8
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  0  8 12 12 12  0  0  4  8 12  8  4  4  0  4 12  0  0  0  4  8  8 12  4  8  8  0 12  8  8 12  0  8  0
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8  4  0  0  4 12  8  0  4 12  0  8  8  8 12 12  8  0  8 12  4  0 12  8  8  8  8 12  8  4  4 12  0  8  4
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  8  0  0  8  8  0  8  0  0  8  0  8  0  0  0  8  0  8  0  8  0  0  8  8
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  8  0  8  0  0  0  0  0  8  8  8  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  8  0  0  8  0  8  8  8  0  8  0  0  8  8  0  0  8  0  8  0  8  8  0  8  8  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+54x^43+113x^44+178x^45+226x^46+248x^47+549x^48+850x^49+1178x^50+1464x^51+1203x^52+874x^53+532x^54+218x^55+131x^56+114x^57+100x^58+56x^59+43x^60+28x^61+10x^62+6x^63+6x^64+4x^65+2x^66+2x^67+1x^68+1x^72

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 37.4 seconds.