The generator matrix

 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  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  1  1  1  1  X  1  1  X  1  1  1  1  1  1  1  1
 0  X  0  0  X  X a*X a^2*X a^4*X a^5*X a^5*X  X a^5*X a^6*X  0 a*X a^5*X a*X a^5*X a^4*X  0 a*X a*X a^2*X a^4*X a^2*X a^6*X  X a^3*X  0  X a^5*X a^2*X  0 a^2*X a*X a^5*X a^2*X a^3*X a^3*X a^4*X a^3*X a*X  X a^3*X  0 a^2*X a^6*X  X a^6*X a^5*X  0  X a^3*X a^5*X a^6*X a*X a^6*X a^3*X a^6*X a^4*X a^2*X  0  0 a^5*X  X a^4*X a^6*X a^6*X a^2*X a^6*X a^2*X a^3*X  0
 0  0  X  0 a^6*X a^5*X a*X a^6*X a^6*X a*X a^6*X a^2*X a*X a^3*X  X a^5*X  X  X a^4*X  X a^3*X a*X a^4*X  0 a^4*X a*X a^6*X a^5*X a*X a*X a^3*X  X a^4*X a*X a^4*X a^5*X  0 a^6*X a^6*X a^3*X a^3*X a^4*X a^6*X a^6*X a*X a^2*X  X a^5*X a^2*X a^4*X a^4*X  X a^3*X  X a*X a^6*X  0 a^4*X  X a^4*X a^3*X a^3*X  X a*X a*X a^4*X a^5*X  X a^3*X a^5*X a^6*X a^2*X a^6*X  X
 0  0  0  X  X a^4*X a^4*X  X a^6*X a^4*X a^6*X a^6*X a^3*X a*X a^4*X a*X a^3*X a^5*X a^6*X a^4*X a^2*X  X  0 a^5*X  0 a^6*X a^3*X  X a*X a*X a^6*X  X a^2*X a^3*X a*X a^4*X  X a^6*X a*X a^5*X  X a^2*X a^3*X a^5*X a^4*X a^2*X a^2*X  0  0 a^3*X  0 a^3*X  X  X  0 a^5*X a^5*X a^5*X a^5*X a*X a^4*X a^5*X a^5*X  0 a*X a^5*X a^6*X  X a^6*X a^6*X a^2*X a*X  0 a^6*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+154x^488+735x^496+1232x^504+6825x^512+22463x^520+406x^528+294x^536+189x^544+175x^552+133x^560+84x^568+63x^576+14x^584

The gray image is a linear code over GF(8) with n=592, k=5 and d=488.
This code was found by Heurico 1.16 in 0.819 seconds.