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

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

Homogenous weight enumerator: w(x)=1x^0+46x^54+260x^55+296x^56+726x^57+637x^58+1538x^59+1310x^60+2590x^61+1667x^62+2712x^63+1278x^64+1488x^65+547x^66+624x^67+225x^68+228x^69+90x^70+44x^71+19x^72+18x^73+20x^74+6x^75+5x^76+6x^77+2x^80+1x^86

The gray image is a code over GF(2) with n=496, k=14 and d=216.
This code was found by Heurico 1.16 in 5 seconds.