The generator matrix

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

generates a code of length 96 over GR(64,4) who´s minimum homogenous weight is 653.

Homogenous weight enumerator: w(x)=1x^0+5992x^653+6832x^654+784x^655+1099x^656+616x^657+1792x^658+1736x^659+2576x^660+20720x^661+16744x^662+5320x^663+2212x^664+504x^665+4256x^666+3080x^667+4592x^668+26488x^669+19544x^670+8960x^671+3885x^672+1176x^673+4032x^674+3416x^675+4592x^676+29792x^677+21336x^678+10024x^679+3941x^680+1288x^681+4256x^682+2520x^683+2576x^684+20944x^685+14392x^686+28x^688+7x^696+21x^704+49x^712+7x^720+7x^728+7x^736

The gray image is a code over GF(8) with n=768, k=6 and d=653.
This code was found by Heurico 1.16 in 78.4 seconds.