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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+28x^42+68x^43+180x^44+242x^45+306x^46+482x^47+872x^48+1208x^49+1645x^50+2142x^51+2150x^52+2086x^53+1666x^54+1202x^55+865x^56+458x^57+266x^58+166x^59+124x^60+96x^61+50x^62+36x^63+29x^64+6x^65+5x^66+2x^68+2x^70+1x^72

The gray image is a code over GF(2) with n=416, k=14 and d=168.
This code was found by Heurico 1.16 in 5.5 seconds.