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  0  2  2  8  1  2  1  8  1  8  2 12  1 12  1  2  1  1  0  1  1  1  8  1  1  1  2  1  1  1  1  0  1  2  1  1  2  1  2  1
 0  2  0  6  0  6  4  2  4 14  2  8  6 14  0  4  6 12 10 12  4  6  2  4  2 14 14  2 14 14  8  2  6  2  6  2  2  2 14  2  0  0  2  0  8  2  2 10  0 14  8  0  8  6 14  2  6 14  0  2  4  0 12  8
 0  0 12  0  0  0  4  8  0  4  4 12  8  4  4 12  4  0 12  4  0  0  8 12  0  0 12 12 12 12 12  8  4  8  4 12  4  8  0  0  0  4  4 12  0  8  8  0  8 12  8  4  4  0 12  8 12  4  8 12  0 12  4  4
 0  0  0 12  0  0  0  4  8  4  4  0  4  4  4  4  0 12  8 12 12  0  4  8 12  8 12  0  4  0  4  0  8  4  4  4  0 12 12  4  4  4  0  8 12  8  8  0  0  8  4  8  8  4  8 12 12  4  0  8  0 12  8  4
 0  0  0  0 12  0  0  0  4  4 12  4 12  8  8  4  8  4  4  8  8 12  4 12 12  4  4  0  8  8  4  4  8  8  8  8  4  4 12  0  8  4 12 12  4  4  8  4  0 12  4 12  4  8  0  0 12 12  8  8  4  0  0 12
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  8  0  8  0  8  0  0  8  8  0  8  8  0  8  0  8  8  0  8  8  8  0  0  8  0  0  8  0  8  0  0  8  0  0  8  8  0  8  0  8
 0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  8  8  0  0  0  8  8  8  0  0  0  0  8  8  0  0  8  0  0  0  8  8  8  0  8  0  8  0  0  8  0  8  0  0  8  8  8  8  8  8  0  8  0  0  8  0  8  8  0

generates a code of length 64 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+109x^54+40x^55+464x^56+208x^57+811x^58+624x^59+1617x^60+1928x^61+3631x^62+4356x^63+5319x^64+4384x^65+3518x^66+1932x^67+1662x^68+616x^69+713x^70+212x^71+334x^72+32x^73+149x^74+4x^75+72x^76+27x^78+2x^80+2x^82+1x^92

The gray image is a code over GF(2) with n=512, k=15 and d=216.
This code was found by Heurico 1.16 in 22.1 seconds.