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

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

Homogenous weight enumerator: w(x)=1x^0+71x^42+184x^44+246x^46+64x^47+519x^48+256x^49+1342x^50+1472x^51+2755x^52+2560x^53+2789x^54+1472x^55+1379x^56+256x^57+493x^58+64x^59+203x^60+144x^62+52x^64+28x^66+25x^68+5x^70+1x^72+2x^74+1x^76

The gray image is a code over GF(2) with n=424, k=14 and d=168.
This code was found by Heurico 1.16 in 63.4 seconds.