The generator matrix

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

generates a code of length 73 over F8[X]/(X^2) who´s minimum homogenous weight is 480.

Homogenous weight enumerator: w(x)=1x^0+182x^480+56x^482+56x^486+392x^487+1897x^488+1120x^490+2128x^493+1680x^494+4368x^495+8477x^496+3584x^498+7056x^501+4032x^502+9632x^503+17857x^504+6608x^506+22512x^509+11760x^510+23408x^511+34426x^512+10696x^514+25648x^517+11144x^518+19544x^519+26243x^520+6608x^522+378x^528+147x^536+168x^544+168x^552+105x^560+56x^568+7x^576

The gray image is a linear code over GF(8) with n=584, k=6 and d=480.
This code was found by Heurico 1.16 in 18.1 seconds.