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

generates a code of length 66 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+63x^54+100x^55+163x^56+272x^57+309x^58+386x^59+553x^60+848x^61+1341x^62+2146x^63+3418x^64+4478x^65+4815x^66+4424x^67+3303x^68+2194x^69+1371x^70+770x^71+489x^72+414x^73+279x^74+188x^75+163x^76+102x^77+65x^78+48x^79+33x^80+12x^81+12x^82+2x^83+5x^84+1x^98

The gray image is a code over GF(2) with n=528, k=15 and d=216.
This code was found by Heurico 1.16 in 28.4 seconds.