The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1  1  1 12  1  1 10  0  1  6  1  1  1  1 10  1 12  6  6  1  1  1 12 10  1  0  1 10  0  1  1 12  1  1  1  2 10  1  1  1 12 10  1 12  0  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5 10 15  1 12  9  1  1  3  1  0  6  5 12  1  6  1  1  1 15 12  9  1  1  3  1 10  1  1  5 10  1  9  6 15  1  1  0  3 10  1  1  3  1  1  0
 0  0  8  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  0  8  0  8  0  8  8  0  0  8  0  8  8  0  8  8  8  8  0  8  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  0  0  8  0  0  8  0  8  8  0  8  8  0  8  8  0  0  8  8  0  0  8  0  8  0  0  0  0  0  8  0  8  0  0  8  8  8  8  8  8  0  8  0  0  0  0  0  0
 0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  8  0  8  8  8  0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  8  8  0  8  8  0  8  8  0  0  8  0  0  8  8  8  0  0  8  0  8  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  0  0  8  8  8  8  8  8  8  8  0  8  8  0  8  0  8  8  0  8  0  8  0  8  0  0  0  8  8  8  0  0  8  8  8  8  8  8  8  8  8  8  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  8  0  8  0  8  0  0  0  0  8  8  8  0  0  8  8  8  0  0  0  8  0  8  8  8  0  8  0  8  8  8  0  0  8  0  0  0  8  0  0  8  8  8  0  0  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  0  8  8  0  0  0  8  8  0  0  8  8  8  8  8  8  0  8  0  0  8  8  0  0  0  8  0  8  8  8  8  8  8  0  8  8  0  8  0  8  0  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+19x^54+24x^55+140x^56+228x^57+419x^58+792x^59+1186x^60+2076x^61+1843x^62+2976x^63+1835x^64+2076x^65+1169x^66+792x^67+400x^68+228x^69+109x^70+24x^71+13x^72+14x^74+6x^76+5x^78+2x^80+5x^82+1x^88+1x^90

The gray image is a code over GF(2) with n=504, k=14 and d=216.
This code was found by Heurico 1.16 in 3.49 seconds.