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

generates a code of length 59 over F8[X]/(X^2) who´s minimum homogenous weight is 384.

Homogenous weight enumerator: w(x)=1x^0+224x^384+700x^392+693x^400+630x^408+28672x^413+420x^416+518x^424+322x^432+217x^440+203x^448+112x^456+49x^464+7x^472

The gray image is a linear code over GF(8) with n=472, k=5 and d=384.
This code was found by Heurico 1.16 in 0.616 seconds.