The generator matrix

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

generates a code of length 87 over GR(64,4) who´s minimum homogenous weight is 576.

Homogenous weight enumerator: w(x)=1x^0+112x^576+224x^581+168x^582+336x^583+637x^584+224x^585+392x^586+3024x^589+2912x^590+2464x^591+4116x^592+1960x^593+2744x^594+8624x^597+6664x^598+5208x^599+8925x^600+5320x^601+5544x^602+12880x^605+18200x^606+7000x^607+23821x^608+11256x^609+11368x^610+21168x^613+24304x^614+9016x^615+22729x^616+9912x^617+8624x^618+11424x^621+5096x^622+4648x^623+224x^624+280x^632+182x^640+168x^648+126x^656+49x^664+42x^672+28x^680

The gray image is a code over GF(8) with n=696, k=6 and d=576.
This code was found by Heurico 1.16 in 22.3 seconds.