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

generates a code of length 59 over F8[X]/(X^2) who´s minimum homogenous weight is 368.

Homogenous weight enumerator: w(x)=1x^0+343x^368+1463x^376+2450x^384+3101x^392+3815x^400+28672x^406+3962x^408+200704x^414+4900x^416+4424x^424+3997x^432+2499x^440+1253x^448+455x^456+105x^464

The gray image is a linear code over GF(8) with n=472, k=6 and d=368.
This code was found by Heurico 1.16 in 36.7 seconds.