The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^45+222x^46+330x^47+771x^48+1400x^49+1556x^50+2824x^51+2092x^52+2894x^53+1625x^54+1326x^55+664x^56+290x^57+160x^58+54x^59+50x^60+22x^61+16x^62+8x^63+4x^64+6x^65+4x^66+2x^67+2x^68+1x^70

The gray image is a code over GF(2) with n=416, k=14 and d=180.
This code was found by Heurico 1.16 in 9.45 seconds.