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

generates a code of length 34 over F9[X]/(X^2) who´s minimum homogenous weight is 243.

Homogenous weight enumerator: w(x)=1x^0+304x^243+288x^248+864x^249+1368x^251+1080x^252+1296x^256+6912x^257+9072x^258+5616x^260+1144x^261+20736x^265+55296x^266+49248x^267+19656x^269+1032x^270+82944x^274+147456x^275+98280x^276+25848x^278+1216x^279+1016x^288+616x^297+152x^306

The gray image is a linear code over GF(9) with n=306, k=6 and d=243.
This code was found by Heurico 1.16 in 17.6 seconds.