The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2  1  1  8  2  1  1  2  1  0  2  1  1  1  2  1  1  1  1  2  1  2  1 12  1  1  2  2  1  1  8  8
 0  2  0  6  4  6 12  2  6 14  8  0  4  2  4 10  6  8  2  6  8  2  2 10 10  0  6  6  2 10  6 10 12 14 10  2 12  8  6  4  2 12  2  2 12 12 12  2  4  4  2
 0  0 12  0  4  0  0  8  4 12  0  4  4  4  8  4  0 12 12  4  8  0  8  4 12  8  0 12  8  8  4  0  8  4  4  8 12  4  8  0  8 12  8  8  0 12  0 12  8  8  4
 0  0  0 12  0  0  0 12  4  8 12 12 12  8  4  4  4 12  4  4 12 12 12 12  8  0  0 12  0  8  4  4  8  0  8  0  8  0  0  4  4  0  0  8  0  0 12  8  8 12  8
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  0  8  8  0  0  8  0  0  8  0  8  8  8  8  8  0  0  8  0  8  8  0  0  0  0  8  8  8  8  8
 0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  8  8  0  0  8  8  8  8  0  8  8  8  0  8  8  8  8  8  0  8  8  0  0  0  0  8  8  8  0  8  8  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  0  0  8  8  8  0  0  0  8  0  0  8  0  0  8  8  8  8  0  8  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+64x^43+180x^44+298x^45+415x^46+686x^47+1194x^48+1814x^49+2302x^50+2572x^51+2324x^52+1722x^53+1244x^54+684x^55+353x^56+230x^57+118x^58+76x^59+40x^60+28x^61+13x^62+14x^63+3x^64+4x^65+4x^66+1x^72

The gray image is a code over GF(2) with n=408, k=14 and d=172.
This code was found by Heurico 1.16 in 11.8 seconds.