The generator matrix

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

generates a code of length 89 over GR(64,4) who´s minimum homogenous weight is 609.

Homogenous weight enumerator: w(x)=1x^0+1008x^609+504x^610+1512x^611+4704x^615+252x^616+4200x^617+1400x^618+2408x^619+1344x^623+119x^624+2016x^625+616x^626+1400x^627+4704x^631+35x^632+3528x^633+1064x^634+1848x^635+84x^640+21x^648

The gray image is a code over GF(8) with n=712, k=5 and d=609.
This code was found by Heurico 1.16 in 64.8 seconds.