The generator matrix

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

generates a code of length 83 over F8[X]/(X^2) who´s minimum homogenous weight is 561.

Homogenous weight enumerator: w(x)=1x^0+3864x^561+504x^563+1344x^564+280x^565+1400x^566+7448x^567+5306x^568+19992x^569+2240x^571+5880x^572+3752x^573+5264x^574+14224x^575+8008x^576+28896x^577+4760x^579+9296x^580+2408x^581+5432x^582+16408x^583+8337x^584+28056x^585+6832x^587+12152x^588+4312x^589+5824x^590+15680x^591+7427x^592+26712x^593+21x^600+56x^608+28x^616

The gray image is a linear code over GF(8) with n=664, k=6 and d=561.
This code was found by Heurico 1.16 in 63.5 seconds.