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

generates a code of length 52 over F9[X]/(X^2) who´s minimum homogenous weight is 387.

Homogenous weight enumerator: w(x)=1x^0+1024x^387+432x^389+576x^393+720x^394+4248x^395+7104x^396+3816x^398+6048x^402+4320x^403+16416x^404+21424x^405+9288x^407+32832x^411+18360x^412+59400x^413+63296x^414+20736x^416+65520x^420+29088x^421+77400x^422+69224x^423+18216x^425+688x^432+664x^441+424x^450+144x^459+32x^468

The gray image is a linear code over GF(9) with n=468, k=6 and d=387.
This code was found by Heurico 1.16 in 28.4 seconds.