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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+62x^54+90x^55+106x^56+166x^57+134x^58+384x^59+119x^60+1494x^61+125x^62+2926x^63+111x^64+1510x^65+96x^66+354x^67+101x^68+126x^69+72x^70+80x^71+44x^72+28x^73+16x^74+6x^75+27x^76+4x^77+4x^78+2x^80+2x^82+1x^84+1x^94

The gray image is a code over GF(2) with n=504, k=13 and d=216.
This code was found by Heurico 1.16 in 1.92 seconds.