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

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

Homogenous weight enumerator: w(x)=1x^0+220x^54+436x^55+725x^56+1186x^57+1701x^58+2384x^59+3256x^60+4634x^61+4162x^62+4248x^63+3241x^64+2476x^65+1616x^66+1028x^67+654x^68+340x^69+197x^70+124x^71+85x^72+34x^73+7x^74+4x^75+6x^76+2x^77+1x^86

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 17.6 seconds.