The generator matrix

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

generates a code of length 44 over F9[X]/(X^2) who´s minimum homogenous weight is 324.

Homogenous weight enumerator: w(x)=1x^0+872x^324+72x^328+1152x^329+720x^330+7600x^333+1296x^336+1728x^337+12096x^338+4320x^339+16232x^342+20736x^345+13824x^346+65664x^347+18360x^348+43560x^351+82944x^354+36864x^355+131040x^356+29088x^357+41512x^360+776x^369+576x^378+352x^387+56x^396

The gray image is a linear code over GF(9) with n=396, k=6 and d=324.
This code was found by Heurico 1.16 in 23.3 seconds.