The generator matrix

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

generates a code of length 48 over F9[X]/(X^2) who´s minimum homogenous weight is 369.

Homogenous weight enumerator: w(x)=1x^0+312x^369+1728x^370+2160x^371+2952x^373+1848x^378+6912x^379+5400x^380+3168x^382+4264x^387+14688x^388+9936x^389+5544x^391+56x^396+32x^405+8x^414+16x^423+24x^432

The gray image is a linear code over GF(9) with n=432, k=5 and d=369.
This code was found by Heurico 1.16 in 0.303 seconds.