The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  1  1  2  8  1  2  1  1  1  0  1  2 12  1  1  0 12  1  0  1  1  1  1  1  1  1 12  4  1  0  8
 0  2  0  6  0  6  8  2  4  6  4 10 14  2  4 12 14  2  8 14  4 10  6  2  4 14 10  6  4  2 12  6  2  2  4  2  2  6  2  4 12 12  0  2 12  4  2 12  8  2  2
 0  0 12  0  0  0 12  0 12  0  4  8  0  8  0  8  0  0  0 12 12  4 12  8 12  4 12 12  8  8  8  8  8 12 12  4 12  0 12 12  0  4  0  4  0  8 12  8  4  4  4
 0  0  0 12  0  0  0  4  8  4  8 12  8  8  0  0  4  4  4  4 12  0 12  0  4  0  8 12  4  8 12 12  0  8  4 12 12  0  0 12 12  4 12  4  0  4  4 12  4  8  0
 0  0  0  0 12  0  4  8  0  4  4 12 12 12  4  8  0  8  8 12  8  4  0 12  4  8  4  0 12  0  8 12  0  0  4  0  4  8  4  4  4  8 12 12  0  0  4  4  8  4  8
 0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  8  8  0  0  8  8  8  8  8  0  8  0  0  0  8  8  8  0  0  8  0  8  0  0  0  8  0  0  0  0  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+66x^43+155x^44+306x^45+456x^46+676x^47+1322x^48+1252x^49+3234x^50+1564x^51+3163x^52+1274x^53+1349x^54+686x^55+364x^56+212x^57+130x^58+62x^59+42x^60+24x^61+14x^62+18x^63+8x^64+4x^65+1x^70+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 4.36 seconds.