The generator matrix

 1  0  1  1  1 14  1  1  4  1  1  4  2  1  1  1  6  1  1 12  1  1 14  1  1  1  0 10  1  1  1  1  1 12  1  1 12 10  1  1  1  1  4 12  2  2  1  1  1  8  2  1 12  2 14  6  1  1  1  2  0  1
 0  1  1  4  7  1  2  3  1  6  5  1  1 14 15  4  1  9  8  1  7  0  1  9 14 15  1  1 15  6  3  2 10  1  8  1  1  1 12 11 13 15  1  1  6  2  0  0  3  2  8 14  1 12  1  1  4 12 10  1  1  0
 0  0  2  2  2  4  2  0  2  0  8  4  2 10  6 12  0 14 10  6 12  6  2  0 12  0  6  8 14  6  6 14  0  8  4 12 10 14  0  4  2  8 12 12  6  2  4 12  8  2 14  4  8 14 14  0  0 14 10 12 14  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  8  8  8  8  8  8  0  8  8  8  8  0  8  0  8  0  8  0  8  0  8  8  8  8  8  0  8  0  0  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  8  0  8  0  0  0  8  8  0  0  8  8  8  8  8  8  0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  8  8  8  8  8  8  8  8
 0  0  0  0  0  8  0  8  8  8  0  0  0  0  8  0  0  0  8  8  8  8  0  0  0  0  8  8  8  0  8  8  8  8  8  8  0  8  0  8  8  0  8  0  8  8  8  0  8  8  8  8  8  0  8  0  0  0  0  8  0  8
 0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  0  8  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  0  0  0  8  8  0  8  8  8  8  0  0  0  0  8  8  8  8  8  8  0  0  8  0  0  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+35x^54+208x^55+506x^56+1154x^57+1700x^58+2768x^59+3291x^60+4610x^61+4365x^62+4702x^63+3400x^64+2656x^65+1475x^66+960x^67+432x^68+276x^69+87x^70+56x^71+42x^72+6x^73+16x^74+8x^75+5x^76+2x^77+1x^78+2x^79+3x^80+1x^82

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 12.4 seconds.