The generator matrix

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

generates a code of length 76 over GR(64,4) who´s minimum homogenous weight is 512.

Homogenous weight enumerator: w(x)=1x^0+2072x^512+504x^514+1568x^515+2576x^516+2744x^517+6664x^518+5600x^519+11935x^520+560x^521+2128x^522+7280x^523+9352x^524+7504x^525+12376x^526+8960x^527+15211x^528+1120x^529+4984x^530+12096x^531+12992x^532+9016x^533+13496x^534+9632x^535+17752x^536+1904x^537+6720x^538+14896x^539+14504x^540+9408x^541+14056x^542+8064x^543+14357x^544+70x^552+28x^560+7x^568+7x^576

The gray image is a code over GF(8) with n=608, k=6 and d=512.
This code was found by Heurico 1.16 in 16.4 seconds.