The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+130x^45+334x^46+824x^47+1409x^48+2490x^49+3780x^50+4804x^51+5381x^52+4736x^53+3786x^54+2506x^55+1363x^56+698x^57+244x^58+136x^59+63x^60+34x^61+14x^62+18x^63+7x^64+8x^65+2x^70

The gray image is a code over GF(2) with n=416, k=15 and d=180.
This code was found by Heurico 1.16 in 77.3 seconds.