The generator matrix

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

generates a code of length 81 over GR(64,4) who´s minimum homogenous weight is 554.

Homogenous weight enumerator: w(x)=1x^0+1568x^554+9408x^559+210x^560+4032x^562+2688x^567+126x^568+2016x^570+9408x^575+133x^576+3136x^578+42x^584

The gray image is a code over GF(8) with n=648, k=5 and d=554.
This code was found by Heurico 1.16 in 0.369 seconds.