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

generates a code of length 86 over F8[X]/(X^2) who´s minimum homogenous weight is 574.

Homogenous weight enumerator: w(x)=1x^0+168x^574+504x^576+56x^577+168x^578+952x^579+2240x^580+1120x^581+1288x^582+889x^584+1680x^585+2240x^586+5152x^587+9744x^588+3976x^589+4760x^590+714x^592+4032x^593+4816x^594+11088x^595+17808x^596+5992x^597+5880x^598+476x^600+11760x^601+11648x^602+23072x^603+33712x^604+11032x^605+10976x^606+343x^608+11144x^609+9800x^610+17080x^611+22512x^612+6552x^613+5600x^614+322x^616+245x^624+203x^632+119x^640+119x^648+70x^656+63x^664+21x^672+7x^688

The gray image is a linear code over GF(8) with n=688, k=6 and d=574.
This code was found by Heurico 1.16 in 41 seconds.