The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 2a^2+2  1  1  1  1  1  1  1  1  1  1 2a^2+2a+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2a^2+2a+2 2a^2+2a+2  1  1  2  1  1 2a  1  1  1  1 2a^2+2a  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2a^2  1  1  1  1  0  1  1  1  1 2a^2+2
 0  1  0  1  a a^2 3a+3 a^2+3a a^2+3a+3 a^2+2a+1 2a^2+2 2a^2+3 a+2 a^2+2  1 3a^2+3a+2  2 a+3 a^2+a+2 2a^2+a+2 2a^2+2a+3 a^2+2a+2 2a^2+3a+1 2a+1 3a^2+3a  1 a^2+3a+1 2a^2+2a+2 2a^2+3a+3 3a  a  3 a^2+3a+3 2a^2+a+1 a^2+a+1 2a^2 3a^2+3a+2 3a^2 a^2+2a+3 2a+3 3a^2+2a+2 2a^2+2a+2  1 a^2+a+2 a^2+2a+2  1 a+3 a^2+a  1 3a^2+a+3 2a^2+2a 2a^2+3a+1 2a^2+3a  1 2a^2+2a+1 2a^2+3a+2 a^2+a+1 3a^2+2a a^2+3a+1 3a^2+3 3a+2 3a^2+3a a^2 3a^2+3a+1  1 2a^2+3a+3 3a^2+2 2a^2+2a+1 3a+2 3a^2+a+3  1 2a^2+1 3a^2+2a+3 2a^2+2  a  1 3a^2+1 3a^2+a+3 2a^2+a+3 3a+1  1
 0  0  1 a^2+2a+1  a 3a^2+3a+2  1 a^2+3a+3 2a^2+3a+1 a^2  3 a^2+a+3 2a^2+2 3a^2+2 a^2+2a+3 2a+1 2a^2+a+1 3a^2+a+2 2a^2+3a a^2+a+2 3a 3a^2+1 2a^2 3a+3 3a^2+3 3a^2+2a+2 3a^2+3a+1 a^2+2a 2a^2+a+3 2a^2+3 a^2+a+1 2a+2 3a^2 a+2 a^2+2a+3 2a^2+3a+2 a^2+3a+2 2a^2+2a+3 a^2+a+1 2a^2+2a+1 2a^2+2a  1 3a^2+a+3 2a^2+a+2 3a^2+a+3 3a+1 a+2 2a+2 2a^2+3  a a^2+a+3 3a^2+2a+3 3a^2+1 a^2+2a a^2+1 2a^2+2 3a^2+3a+3 2a^2+a+2  2 3a^2+2a+1 2a^2+2a+3 3a+1 3a^2+3a+1 a+1 2a^2+2a 3a^2 2a+3 2a^2+3a+3 2a^2+3a+1 a^2+3  0  2  3 a^2+a+2 3a+2 a+3 3a+3 a^2+a 3a^2+a+1 2a^2+1 3a^2+2a+3

generates a code of length 81 over GR(64,4) who´s minimum homogenous weight is 547.

Homogenous weight enumerator: w(x)=1x^0+3472x^547+168x^549+1288x^550+1456x^551+4606x^552+4928x^553+5320x^554+17136x^555+1176x^557+6272x^558+6160x^559+10976x^560+8512x^561+7504x^562+24136x^563+2520x^565+11816x^566+8400x^567+13335x^568+8512x^569+8456x^570+26208x^571+3304x^573+12880x^574+9072x^575+14476x^576+10304x^577+7392x^578+22232x^579+49x^584+63x^592+14x^600

The gray image is a code over GF(8) with n=648, k=6 and d=547.
This code was found by Heurico 1.16 in 38.6 seconds.