The generator matrix

 1  0  1  1  1 14  1  1  8  1  6  1  8  1  1  1 10  1  1  1 14  1  1  2  1 12 14  1  1  8 12  1  1  1  1 10  1  4  1  1  1  0  8  1 10  1  2  1  8  6  2  1
 0  1 11  6  1  1  0  3  1  6  1  5  1 11  2  9  1  0  2  5  1  7  6  1  8  1  1  2  9  1  1 12 13 12 15  1  3  1  3 10 11  1  1  9  1 12  2  2  1  1  8  0
 0  0 12  0  0  0  0  4  0  8  8  4  0  4  8 12  8  8  8  0  4  0  4  4  4 12  4 12  8  4  0 12 12  8  4  0  4  8  8  4 12  4  4  8 12  4 12  0  8  0  0  0
 0  0  0 12  0  0  0  0  8  4  4  4  4  4  4  8  8  4  0  8  4 12  8  4  8  0  0  4 12  8 12  4 12  4 12 12  8  4  8 12  4  8 12 12  0 12  0  4  8  4  4  0
 0  0  0  0  4  4 12  4 12 12  4  8  8  4  0 12  8 12 12  8 12  0 12  4  8 12  8  4  4  8  4  0  4  4  0 12  4  0  0  8  8  4 12 12  4 12  4  8  4  4  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  0  0  0  8  0  8  8  8  8  0  0  0  0  8  0  0  0  8  8  8  8  0  0  0  8  8  0  0  0
 0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  8  0  0  0  8  0  0  0  8  0  0  0  8  8  8  8  0  0  8  0  8  8  0  0  8  8  0  0  0  8  8  0  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+53x^42+110x^43+218x^44+308x^45+529x^46+1486x^47+2467x^48+5392x^49+6644x^50+11132x^51+8960x^52+11204x^53+6477x^54+5360x^55+2503x^56+1424x^57+570x^58+318x^59+167x^60+96x^61+52x^62+26x^63+17x^64+8x^65+9x^66+3x^68+2x^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 38.7 seconds.