The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+35x^54+100x^55+249x^56+552x^57+866x^58+1688x^59+2488x^60+3704x^61+4676x^62+4358x^63+4426x^64+3746x^65+2507x^66+1602x^67+834x^68+486x^69+200x^70+74x^71+55x^72+38x^73+30x^74+14x^75+10x^76+18x^77+4x^78+4x^79+1x^80+1x^82+1x^86

The gray image is a code over GF(2) with n=504, k=15 and d=216.
This code was found by Heurico 1.16 in 13.5 seconds.