The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1  1 10  1  1  0  1  1  1  1  6  1 10  1  1  6  1 10  1  1  1  1  1  1  1 12  1 12  6  6  0  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 15 12  1  9 10  1  0  3  6 10  1  5  1 15  3  1 12  1  6 10 15  9  5  6  3  1  6  2  1  1  1  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  8  8  0  8  8  0  0  0  0  0  8  0  8  8  0  8  8  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  0  8  0  8  8  8  8  8  0  0  8  0  8  8  0  0  8  8  8  8  8  8  8  0  8  8  8  0  0  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  0  8  0  8  8  8  8  8  8  8  0  8  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  8  8  8  0  0  8  0  0  8  8  8  8  8  8  8  8  8  0  0  8  8  0  0  8  8  8  0  8  0
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  8  8  0  0  8  8  0  8  0  8  8  0  0  8  0  0  8  8  8  0  0  0  8  8  8  0  0  8  0
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  0  8  0  8  8  0  8  8  8  8  8  8  8  8  0  0  8  0  0  8  0  8  8  8  0  0  8  0  0  8  8  0  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  0  8  8  0  0  8  8  8  0  0  8  8  8  0  8  0  0  0  0  8  0  0  8  8  0  0  8  8  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+26x^42+12x^43+78x^44+162x^45+286x^46+632x^47+1189x^48+2684x^49+3273x^50+5740x^51+4660x^52+5696x^53+3301x^54+2708x^55+1159x^56+644x^57+244x^58+120x^59+54x^60+30x^61+24x^62+4x^63+18x^64+9x^66+8x^68+5x^70+1x^72

The gray image is a code over GF(2) with n=416, k=15 and d=168.
This code was found by Heurico 1.16 in 9.97 seconds.