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

generates a code of length 67 over GR(64,4) who´s minimum homogenous weight is 424.

Homogenous weight enumerator: w(x)=1x^0+546x^424+1568x^432+2730x^440+3164x^448+3584x^455+3633x^456+50176x^463+3864x^464+175616x^471+4172x^472+4312x^480+3696x^488+2660x^496+1610x^504+595x^512+189x^520+28x^528

The gray image is a code over GF(8) with n=536, k=6 and d=424.
This code was found by Heurico 1.16 in 43.5 seconds.