The generator matrix

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

generates a code of length 96 over F9[X]/(X^2) who´s minimum homogenous weight is 729.

Homogenous weight enumerator: w(x)=1x^0+152x^729+72x^731+216x^737+840x^738+864x^740+1512x^741+1728x^742+2160x^744+3528x^746+2632x^747+3240x^749+16704x^750+9504x^751+5904x^753+7776x^755+6496x^756+7704x^758+34128x^759+19440x^760+12096x^762+12312x^764+20432x^765+17712x^767+85536x^768+42336x^769+19440x^771+18504x^773+26504x^774+22896x^776+72072x^777+31968x^778+12888x^780+10152x^782+504x^783+424x^792+296x^801+312x^810+248x^819+96x^828+56x^837+40x^846+16x^855

The gray image is a linear code over GF(9) with n=864, k=6 and d=729.
This code was found by Heurico 1.16 in 58 seconds.