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

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

Homogenous weight enumerator: w(x)=1x^0+52x^42+70x^43+154x^44+204x^45+222x^46+338x^47+535x^48+996x^49+1704x^50+2516x^51+2870x^52+2516x^53+1735x^54+982x^55+502x^56+286x^57+219x^58+164x^59+100x^60+78x^61+58x^62+24x^63+30x^64+14x^65+9x^66+2x^67+2x^69+1x^78

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 5.4 seconds.