The generator matrix

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

generates a code of length 51 over F9[X]/(X^2) who´s minimum homogenous weight is 378.

Homogenous weight enumerator: w(x)=1x^0+512x^378+288x^385+4968x^386+3680x^387+3024x^394+30456x^395+12592x^396+16416x^403+128304x^404+40224x^405+32760x^412+203688x^413+52480x^414+800x^423+616x^432+408x^441+192x^450+32x^459

The gray image is a linear code over GF(9) with n=459, k=6 and d=378.
This code was found by Heurico 1.16 in 28.7 seconds.