The generator matrix

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

generates a code of length 72 over GR(64,4) who´s minimum homogenous weight is 472.

Homogenous weight enumerator: w(x)=1x^0+77x^472+112x^474+168x^479+973x^480+504x^481+1456x^482+1064x^486+5040x^487+5152x^488+2408x^489+6160x^490+3528x^494+12096x^495+10262x^496+5880x^497+11984x^498+11256x^502+35280x^503+23989x^504+11256x^505+22848x^506+12824x^510+33432x^511+19964x^512+8624x^513+14784x^514+315x^520+196x^528+154x^536+168x^544+133x^552+28x^560+28x^568

The gray image is a code over GF(8) with n=576, k=6 and d=472.
This code was found by Heurico 1.16 in 17.4 seconds.