The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+230x^53+473x^54+710x^55+564x^56+400x^57+481x^58+556x^59+326x^60+202x^61+52x^62+46x^63+20x^64+28x^65+4x^69+1x^72+1x^74+1x^78

The gray image is a code over GF(2) with n=456, k=12 and d=212.
This code was found by Heurico 1.16 in 0.289 seconds.