The generator matrix

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

generates a code of length 59 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+36x^52+104x^53+84x^54+202x^55+175x^56+602x^57+356x^58+1012x^59+339x^60+614x^61+175x^62+172x^63+76x^64+86x^65+15x^66+20x^67+13x^68+2x^69+8x^70+2x^71+1x^74+1x^102

The gray image is a code over GF(2) with n=472, k=12 and d=208.
This code was found by Heurico 1.16 in 0.458 seconds.