The generator matrix

 1  0  0  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 a^3*X  1  1 a^5*X  1  0  1  1 a*X  1  1  1  1  1  1  1  1  1  1  1
 0  1  0 a^7*X+1  a a^2 a^7*X+2 a^7*X+a^7  X a^7*X+a a^6 a^6*X+1 a^7*X+a^2 a^7*X+a^3 a^7 X+a^2 a^7*X+a^5  2 a^3 X+a^6 a^6*X a^5 a^7*X+a^6 a^6*X+a^7 a^3*X+1 a^5*X+a^3 a*X+a a^6*X+a^2 X+1 a^5*X+a a*X+a^6  1 a^2*X X+a^3  1 a^6*X+a^5  1 2*X+2 a^2*X+2  1 a^3*X+a a^2 X+a^7 a^6*X+a^3 a^6*X+a^2 a^6*X+1 a^3*X+a^5 a^6*X+2 a^6*X a^6*X+a^5  0
 0  0  1 a^7*X+a^7  a a^6 a^7*X+a^5 a^7*X+2 a^7*X+a^3 a^7*X+a^2 X+a^6 a^3 a^6*X+a^7 a^6*X+a^2 X+a a^5*X+2 a^3*X+1 a*X+1 a^6*X+a^5 a*X+a^2 X+1 a^3*X 2*X+a^3 a*X+a^6  X a^2*X+2 2*X a^5 a*X+a a^7*X+1  2 a*X+a^6 a^6*X+a X+a^7 a^5*X+a X+2 a^5*X+1 a^5*X+a^2 a^5*X+a^6 a^2*X+a^3 a^5*X+a^7 a^2*X+a^2 a^2*X+a^3 a^5*X+a a*X X+a^5 a*X+a^7 a^2*X+a^3 2*X+a^7 a^5*X+a^5 a^2*X

generates a code of length 51 over F9[X]/(X^2) who´s minimum homogenous weight is 387.

Homogenous weight enumerator: w(x)=1x^0+1664x^387+4032x^388+144x^389+504x^392+13680x^395+35040x^396+24336x^397+1512x^398+1944x^400+8064x^401+34200x^404+69488x^405+48096x^406+1728x^407+15552x^409+32256x^410+62928x^413+110240x^414+63504x^415+2448x^416+56x^441+24x^450

The gray image is a linear code over GF(9) with n=459, k=6 and d=387.
This code was found by Heurico 1.16 in 24.6 seconds.