The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+64x^54+264x^55+562x^56+994x^57+1706x^58+2606x^59+3851x^60+3976x^61+4708x^62+4320x^63+3753x^64+2538x^65+1583x^66+922x^67+455x^68+148x^69+153x^70+68x^71+41x^72+24x^73+7x^74+12x^75+6x^76+3x^78+3x^80

The gray image is a code over GF(2) with n=496, k=15 and d=216.
This code was found by Heurico 1.16 in 12.5 seconds.