The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1 a^2*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^6*X+a^6 a^6*X+1 a^5 a^3  a a^6*X+a^4 a^3 a^6*X+a^6 a^6*X+1 X+a a^6*X+1 a^5  0 a^5*X+a^4  1 X+a^3 X+a^3 a^4*X+1 X+a a^6*X+a^2 X+a^3  1 X+a X+a^5 X+a^5  a a^4*X+1 a^5*X+a^2 a*X+a a*X+a^3 a^2*X+a^3 a^5*X+a^6 a^2*X+a^2  X a*X+a  1 a^5*X+a^6 a^2*X+a^4 a^2*X+a^3 a^3 a^3*X+a a*X+a^2 a^2*X+a^6 a*X  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  0 a^2*X a^4*X a^3*X  0 a*X a^3*X a^5*X a*X  X  X a*X a^3*X a^6*X  0  X a^6*X a^6*X a*X a^2*X a^4*X  0 a^5*X a^4*X a^3*X a*X  0 a*X a^4*X a^4*X a*X a^3*X a*X a^3*X a^6*X a^6*X a*X  X  0 a^6*X  0 a*X a^2*X  0 a^3*X  X
 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^4*X  0 a^3*X a*X a^3*X a^5*X  X a^2*X  X a*X a^3*X  0 a^4*X a^5*X a^6*X  0  X a^5*X a*X a^3*X a^4*X  X a*X a^2*X  0 a^4*X a^2*X a^5*X a*X a^5*X  X a^3*X a^6*X a^2*X a^3*X  X a^2*X  X a^2*X  0  0 a^3*X  0 a^2*X a^2*X a^3*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+210x^384+56x^387+1400x^391+637x^392+1624x^394+3976x^395+6888x^399+735x^400+8568x^402+14616x^403+11256x^407+707x^408+31752x^410+44632x^411+22904x^415+448x^416+44072x^418+51408x^419+14896x^423+392x^424+399x^432+238x^440+175x^448+91x^456+56x^464+7x^472

The gray image is a linear code over GF(8) with n=472, k=6 and d=384.
This code was found by Heurico 1.16 in 14.4 seconds.