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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+136x^42+20x^43+443x^44+108x^45+711x^46+504x^47+1258x^48+1468x^49+2672x^50+1936x^51+2445x^52+1444x^53+1408x^54+584x^55+592x^56+52x^57+334x^58+28x^59+157x^60+49x^62+29x^64+2x^66+3x^68

The gray image is a code over GF(2) with n=408, k=14 and d=168.
This code was found by Heurico 1.16 in 5.41 seconds.