The generator matrix

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

generates a code of length 79 over GR(64,4) who´s minimum homogenous weight is 533.

Homogenous weight enumerator: w(x)=1x^0+2408x^533+112x^534+336x^535+763x^536+1792x^537+5264x^538+6720x^539+4144x^540+13720x^541+728x^542+1008x^543+5418x^544+7336x^545+14280x^546+12488x^547+5208x^548+21392x^549+2688x^550+2352x^551+6307x^552+8624x^553+16128x^554+13104x^555+6720x^556+19320x^557+3640x^558+3472x^559+9401x^560+10920x^561+18088x^562+14280x^563+5432x^564+18424x^565+56x^568+42x^576+14x^584+14x^592

The gray image is a code over GF(8) with n=632, k=6 and d=533.
This code was found by Heurico 1.16 in 17.2 seconds.