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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+53x^42+108x^44+150x^46+186x^48+236x^50+1334x^52+4096x^53+1325x^54+247x^56+175x^58+112x^60+72x^62+44x^64+30x^66+14x^68+5x^70+1x^72+2x^74+1x^80

The gray image is a code over GF(2) with n=424, k=13 and d=168.
This code was found by Heurico 1.16 in 2.03 seconds.