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

generates a code of length 74 over F8[X]/(X^2) who´s minimum homogenous weight is 488.

Homogenous weight enumerator: w(x)=1x^0+217x^488+56x^492+336x^494+784x^495+2170x^496+896x^500+3584x^501+4592x^502+5712x^503+7028x^504+3696x^508+8064x^509+9296x^510+10416x^511+12964x^512+11200x^516+23296x^517+23632x^518+23408x^519+22659x^520+12824x^524+22400x^525+19488x^526+17024x^527+15344x^528+350x^536+252x^544+217x^552+98x^560+70x^568+35x^576+35x^584

The gray image is a linear code over GF(8) with n=592, k=6 and d=488.
This code was found by Heurico 1.16 in 17.7 seconds.