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

generates a code of length 61 over F8[X]/(X^2) who´s minimum homogenous weight is 384.

Homogenous weight enumerator: w(x)=1x^0+616x^384+1820x^392+2716x^400+3367x^408+3584x^413+3745x^416+50176x^421+4179x^424+175616x^429+4536x^432+4354x^440+3570x^448+2415x^456+1050x^464+329x^472+70x^480

The gray image is a linear code over GF(8) with n=488, k=6 and d=384.
This code was found by Heurico 1.16 in 37.8 seconds.