The generator matrix

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

generates a code of length 77 over GR(64,4) who´s minimum homogenous weight is 519.

Homogenous weight enumerator: w(x)=1x^0+1904x^519+175x^520+392x^521+1624x^522+2800x^523+3752x^524+4984x^525+7112x^526+11928x^527+413x^528+1736x^529+8176x^530+9408x^531+8792x^532+8120x^533+10696x^534+15064x^535+1463x^536+3416x^537+13272x^538+12208x^539+11480x^540+9128x^541+11480x^542+17864x^543+1862x^544+5208x^545+16352x^546+15008x^547+11816x^548+10024x^549+10136x^550+14168x^551+77x^552+77x^560+21x^568+7x^576

The gray image is a code over GF(8) with n=616, k=6 and d=519.
This code was found by Heurico 1.16 in 16.5 seconds.