The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+82x^53+562x^54+612x^55+902x^56+444x^57+534x^58+232x^59+259x^60+174x^61+185x^62+28x^63+37x^64+28x^65+14x^66+1x^68+1x^70

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 0.172 seconds.