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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+30x^54+40x^55+97x^56+688x^57+97x^58+40x^59+30x^60+1x^114

The gray image is a code over GF(2) with n=456, k=10 and d=216.
This code was found by Heurico 1.16 in 0.243 seconds.