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

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

Homogenous weight enumerator: w(x)=1x^0+36x^42+231x^44+36x^45+308x^46+124x^47+1020x^48+212x^49+2006x^50+268x^51+2049x^52+236x^53+949x^54+116x^55+337x^56+28x^57+120x^58+4x^59+61x^60+30x^62+9x^64+6x^66+3x^68+1x^70+1x^72

The gray image is a code over GF(2) with n=408, k=13 and d=168.
This code was found by Heurico 1.16 in 1.35 seconds.