The generator matrix

 1  0  1  1  1  6  1  1  0  1 14  1  1  1  0  1 14  1  1  1  6  1 12  1  1  1  8  1 12  1  1  1  1 10  1 12 14  1  2  1  1  1  1  1  4  1  1  1  2  1  2  1
 0  1 11  6  1  1  8  5  1  3  1  6 11  0  1  5  1 14  9  0  1  1  1 12  9 14  1  1  1  6  3  4 12  1 11  1  1  2 12  3  1  1  2 11  1  2  3 15  6  0  0  0
 0  0 12  0  0  0  0  0  0  0  0  8  8  4 12 12  4 12 12 12  4 12  4  8  8  4 12  4  4  4  4  8 12 12  8  4  4 12 12  8  8  4  8  8  0  8  0  4 12 12  4  0
 0  0  0 12  0  0  0  0  4  4 12 12 12 12 12  8 12 12  4  8  0 12  4  0  8  0  4  4 12 12  4  4  8  0 12  4  4  4  4  4  4  8  4  4  4  4 12  8  8  4  8  0
 0  0  0  0  4  0  8  4  0  4  0  0  4 12  4  8 12 12  0 12  4  8  4  8 12  0  0 12  8  8 12 12  0  8  0  8 12  8 12  0  8 12  4 12  0  8 12  4  8  4 12  0
 0  0  0  0  0 12 12  4 12  8  8  4 12 12  4  4  0  8  8  8  0 12 12  8  4  8 12  0  8  0  4 12 12 12  8  8  4  4  4  0 12  4  4  4  0 12  4  8 12 12  8  0

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

Homogenous weight enumerator: w(x)=1x^0+38x^42+100x^43+252x^44+376x^45+663x^46+1482x^47+2448x^48+4812x^49+7352x^50+9514x^51+11356x^52+9838x^53+7273x^54+4754x^55+2438x^56+1434x^57+648x^58+306x^59+182x^60+106x^61+79x^62+36x^63+25x^64+10x^65+10x^66+2x^68+1x^70

The gray image is a code over GF(2) with n=416, k=16 and d=168.
This code was found by Heurico 1.16 in 39.5 seconds.