The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+84x^55+174x^56+498x^57+829x^58+1376x^59+1746x^60+2426x^61+2255x^62+2408x^63+1702x^64+1350x^65+795x^66+460x^67+123x^68+66x^69+17x^70+12x^71+23x^72+8x^73+4x^74+12x^75+7x^76+4x^77+3x^78+1x^94

The gray image is a code over GF(2) with n=496, k=14 and d=220.
This code was found by Heurico 1.16 in 13.5 seconds.