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

generates a code of length 55 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+172x^53+138x^54+456x^55+102x^56+108x^57+14x^58+32x^59+1x^104

The gray image is a code over GF(2) with n=440, k=10 and d=212.
This code was found by Heurico 1.16 in 33.1 seconds.