The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  0  1  1  1  1  1  1  2 12  1  1  1  1  1  2  0  1  1  1  2  1 12  1  0  1  1  2  2 12  0 12 12  1  0  2  1  2
 0  2 12  6  0  6 12 10  0  6 12 10  4 10  6  0  8 14 12  6 10  6  0 12 10  2 14 12 10  0 10  0 10  2  6  8 12  0  0  6  2 12  8 10 10  2  2  6  2  4 12  6 10  2  2  2  2  2  2  0  8 12
 0  0  8  0  0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  8  8  8  0  8  0  0  8  8  0  8  0  8  0  8  0  0  8  0  8  8  0  0  0  0  8  8  0  0  8  8  8  0  0  8  0  8  0  8  8
 0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  8  8  8  0  8  8  0  0  8  8  0  0  8  0  0  0  0  0  8  0  0  8  0  0  0  8  0  8  8  0  8  0  8  8  8  0  8  8  0  0  0  8  0  8  0  8
 0  0  0  0  8  0  0  0  8  0  0  8  0  8  8  0  8  8  0  8  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  8  0  0  0  0  8  8  8  0  8  8  8  0  8  0  8  8  0  0  0  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  8  0  8  0  8  8  8  8  0  8  0  8  0  8  0  0  8  0  8  8  8  0  8  0  0  0  8  8  0  0  8  0  0  8  8  0  0  8  0  0  8  8  8  0  8  8  8  8  0  0  8
 0  0  0  0  0  0  8  0  8  0  8  0  0  0  8  0  0  8  8  8  8  8  0  8  0  8  8  0  8  0  0  8  8  0  0  8  0  0  0  8  0  0  0  8  0  8  0  8  0  8  8  8  0  8  8  8  0  0  0  8  0  8
 0  0  0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  8  0  8  0  0  0  8  8  8  0  0  0  8  0  0  0  8  8  8  8  0  8  8  0  0  0  0  0  8  8  8  8  8  0  0  0  0  0  0  8  8  8  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+76x^54+349x^56+64x^57+495x^58+576x^59+769x^60+1408x^61+763x^62+1408x^63+756x^64+576x^65+512x^66+64x^67+256x^68+60x^70+34x^72+9x^74+7x^76+5x^78+3x^80+1x^88

The gray image is a code over GF(2) with n=496, k=13 and d=216.
This code was found by Heurico 1.16 in 1.59 seconds.