The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2  1  1  8  2  1  1  2  1  0  2  1  1  4  1  1  1  4  1  1  1  1 12  4  1  1  1  2  1  1  1  1  1  2
 0  2  0  6  4  6 12  2  6 14  8  0  4  2  4 10  6  8  2  6  8  2  2 10 10  0  6  6  2 10  6  4  2 12 10 14  2  8  2  8  4  2  0  6  8  4  2 12  4  6  2 12 14
 0  0 12  0  4  0  0  8  4 12  0  4  4  4  8  4  0 12 12  4  8  0  8  4 12  8  0 12  8  8  4  4  4  0 12 12  0  8  0  8 12  4 12  8  8  4  8  4  4  4 12  0  8
 0  0  0 12  0  0  0 12  4  8 12 12 12  8  4  4  4 12  4  4 12 12 12 12  8  0  0 12  0  8 12  4  0  0  4  0 12  4  4  8  8  4  0  4  0 12 12 12 12  8  4 12  4
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  0  8  8  0  0  8  0  0  8  8  0  0  8  8  0  0  8  8  8  8  0  8  8  8  8  8  0  0  0  0  8  8
 0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  8  8  0  0  8  8  8  8  0  8  8  8  0  8  0  0  0  0  8  8  8  0  8  8  0  8  8  0  0  0  0  0  0  0  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  0  0  8  8  0  0  8  8  0  8  0  8  0  0  8  8  0  8  0  8  0  0  8  0  8  0  0

generates a code of length 53 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+88x^45+169x^46+250x^47+484x^48+492x^49+1606x^50+1056x^51+3400x^52+1346x^53+3392x^54+1150x^55+1618x^56+418x^57+398x^58+194x^59+104x^60+78x^61+63x^62+32x^63+24x^64+10x^65+4x^66+6x^67+1x^80

The gray image is a code over GF(2) with n=424, k=14 and d=180.
This code was found by Heurico 1.16 in 50.5 seconds.