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

generates a code of length 40 over F9[X]/(X^2) who´s minimum homogenous weight is 288.

Homogenous weight enumerator: w(x)=1x^0+240x^288+216x^296+2080x^297+720x^298+2808x^299+648x^304+5184x^305+8960x^306+4320x^307+11016x^308+10368x^313+41472x^314+51752x^315+18360x^316+39528x^317+41472x^322+110592x^323+98824x^324+29088x^325+51624x^326+944x^333+688x^342+456x^351+80x^360

The gray image is a linear code over GF(9) with n=360, k=6 and d=288.
This code was found by Heurico 1.16 in 21.5 seconds.