The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+50x^52+240x^53+440x^54+558x^55+560x^56+488x^57+524x^58+514x^59+410x^60+228x^61+37x^62+14x^63+16x^64+4x^65+3x^66+2x^67+3x^70+2x^72+1x^74+1x^80

The gray image is a code over GF(2) with n=456, k=12 and d=208.
This code was found by Heurico 1.16 in 0.272 seconds.