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  1  1  2  2  2  1  1  2  1  1  1  1  1  1  1  2  1  1  1  2  1  4  2  1  1  1  4  0  4  1  1  4  2  4
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  8  8  0  0 12  4  0  4  4  0 12  8  4  0  8 12  8  8  0  4 12  4  0 12  0  8  8  0  4 12  4  4  0  8 12  8 12  8  4 12  0  8  8  8  8
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  0  8 12 12 12  0  0  4  8  8  4  0  0  4  4  8  0 12  0  8  4 12 12  8 12  4 12 12  0  8  4  0 12  4 12 12  8  8  0  4  4 12 12  0  4
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8  4  0  0  4 12  8  0  4 12  8  8 12 12  4  8  0  8  0 12 12  0  8  4  4  4  4 12  0  8 12  8  8  8  0  0  8  0 12  8 12  0  0  4  4  0
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  0  8  8  8  0  0  8  0  8  0  8  0  8  8  0  0  0  0  0  0  8  8  0  0  8  0  0  0  8  8  8  8  8  0  8
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  0  0  8  0  8  8  0  0  0  0  0  0  0  0  8  0  0  0  8  8  0  0  0  8  8  8  8  0  8  0  0  0  8  0  8  8  8
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  8  0  0  0  8  0  8  0  8  0  8  8  8  8  0  8  0  8  0  8  0  0  8  8  8  0  0  8  0  0  8  0  8  8  8  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+168x^54+8x^55+288x^56+96x^57+461x^58+272x^59+1002x^60+1160x^61+1411x^62+1160x^63+959x^64+272x^65+381x^66+96x^67+229x^68+8x^69+101x^70+67x^72+34x^74+13x^76+4x^78+1x^96

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 8.61 seconds.