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

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

Homogenous weight enumerator: w(x)=1x^0+140x^53+130x^54+388x^55+225x^56+462x^57+170x^58+244x^59+65x^60+108x^61+35x^62+56x^63+12x^64+10x^65+1x^70+1x^92

The gray image is a code over GF(2) with n=456, k=11 and d=212.
This code was found by Heurico 1.16 in 0.234 seconds.