The generator matrix

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

generates a code of length 58 over F8[X]/(X^2) who´s minimum homogenous weight is 389.

Homogenous weight enumerator: w(x)=1x^0+3248x^389+5600x^390+3472x^391+63x^392+504x^393+336x^394+3360x^395+3360x^396+20664x^397+20440x^398+8120x^399+168x^400+3024x^401+1120x^402+6720x^403+4032x^404+30464x^405+28336x^406+9632x^407+182x^408+7224x^409+2128x^410+11424x^411+6944x^412+38808x^413+31640x^414+11032x^415+28x^416+42x^424+7x^432+21x^440

The gray image is a linear code over GF(8) with n=464, k=6 and d=389.
This code was found by Heurico 1.16 in 11.3 seconds.