The generator matrix

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

generates a code of length 44 over F9[X]/(X^2) who´s minimum homogenous weight is 339.

Homogenous weight enumerator: w(x)=1x^0+5040x^339+3240x^340+288x^342+12600x^348+5184x^349+256x^351+23184x^357+9072x^358+104x^360+16x^369+16x^378+16x^387+32x^396

The gray image is a linear code over GF(9) with n=396, k=5 and d=339.
This code was found by Heurico 1.16 in 8.7 seconds.