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

generates a code of length 72 over F8[X]/(X^2) who´s minimum homogenous weight is 472.

Homogenous weight enumerator: w(x)=1x^0+77x^472+112x^474+168x^479+973x^480+504x^481+1456x^482+1064x^486+5040x^487+5152x^488+2408x^489+6160x^490+3528x^494+12096x^495+10262x^496+5880x^497+11984x^498+11256x^502+35280x^503+23989x^504+11256x^505+22848x^506+12824x^510+33432x^511+19964x^512+8624x^513+14784x^514+315x^520+196x^528+154x^536+168x^544+133x^552+28x^560+28x^568

The gray image is a linear code over GF(8) with n=576, k=6 and d=472.
This code was found by Heurico 1.16 in 17.2 seconds.