The generator matrix

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

generates a code of length 36 over F9[X]/(X^2) who´s minimum homogenous weight is 270.

Homogenous weight enumerator: w(x)=1x^0+96x^270+432x^272+3456x^273+11232x^274+17280x^275+12960x^276+192x^279+2592x^280+6912x^281+24192x^282+44928x^283+43200x^284+20736x^285+17704x^288+20736x^289+27648x^290+65664x^291+95472x^292+79488x^293+36288x^294+128x^297+48x^306+32x^315+24x^324

The gray image is a linear code over GF(9) with n=324, k=6 and d=270.
This code was found by Heurico 1.16 in 45.1 seconds.