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  X  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  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  a a^6*X+a^2 a^3 a^6*X+a^4 a^5 a^6*X+a^6  a a^6*X+a^2 a^6*X+a^4  1  0 a^3 a^6*X+a^6 a^6*X+1 a^5 a^6*X+a^6  a  1 a^6*X+a^4  0 a^6*X+a^2 a^5 X+a^3 a^6*X+1 a^5*X+a^2  X a^3  1 X+a^3 X+a  X a^5*X+a^4 X+a^5 a^5*X+a^6 a^5*X+a^2 a^4*X+a^4 a*X+a a^6*X+1  X a^4*X+a^6 a*X+a^5 a^5*X+1 X+1 X+a^5 a*X X+a a^2*X+a^3 X+a^5 X+a^4 a^6*X+1 a^5*X a^4*X+1 X+a^3 a^5*X+a^2 a^3*X+a^2 a^6*X a^3*X+a^6 a^5*X+1 a^4*X+a^4 a^3 a^6 a^5 X+a^3 a*X+a^5 a^4*X+a^3  1 a^4*X a*X+a^5 a^5*X+a^3 a^4*X+1 a^5*X+a^3 a^6*X+1 a^6*X+a^5 a^4*X+a^5 a^4*X+a^4 a^4*X+a^4 a^4*X+1 a^5*X+a^2 a^5*X+1 a*X a^2*X+a a^4*X+1 X+a^5  0
 0  0 a^6*X  0  X  X a^3*X  X a^2*X a^3*X a^6*X a^2*X  X a^4*X a^5*X  0 a^6*X  X a^5*X a*X a*X a^4*X a^3*X  X a^5*X a^6*X a^5*X a^5*X a^4*X  X a^4*X a^4*X a^4*X a^5*X a*X a^5*X a*X a^2*X a^2*X  0  0  X  0 a^5*X a^3*X a^4*X a^4*X  0 a^3*X a^4*X a^4*X  X a^5*X a^3*X a^3*X a^2*X  0  X a^6*X a^2*X a^2*X a^4*X a^5*X  X a^4*X a^3*X a^3*X a^5*X a^4*X  0 a^3*X  0 a*X  X  0 a^4*X a*X a^2*X a^6*X a^3*X a^5*X a^6*X a*X a^5*X a^2*X a^3*X  0
 0  0  0  X a^6*X a^5*X a^3*X a^2*X a^5*X a^6*X a^6*X a^6*X a^5*X a^3*X a^3*X a^2*X a^2*X a*X a^2*X  X  0 a^4*X a*X  X a*X a^4*X  X a^6*X  0 a*X a^6*X  X a^3*X a^4*X a^4*X  0 a*X  X a^3*X a^4*X  X a^5*X a*X a^2*X a^3*X a^5*X a^6*X a^6*X a^4*X a^3*X a^4*X a^6*X a^3*X a^5*X  0  0 a^2*X a^3*X  0 a^4*X  0 a^5*X a^4*X  X  X  0 a^3*X  0 a^3*X a^4*X a*X  X a^5*X a^3*X a^2*X a^2*X  0 a^2*X a^4*X a^2*X a^5*X  X  X a^3*X a^6*X  X a*X

generates a code of length 87 over F8[X]/(X^2) 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 linear code over GF(8) with n=696, k=6 and d=576.
This code was found by Heurico 1.16 in 22.2 seconds.