The generator matrix

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

generates a code of length 87 over F9[X]/(X^2) who´s minimum homogenous weight is 657.

Homogenous weight enumerator: w(x)=1x^0+136x^657+144x^661+816x^666+432x^668+864x^669+3456x^670+1584x^671+3920x^675+6048x^677+7560x^678+13968x^679+4680x^680+11952x^684+15552x^686+18792x^687+28584x^688+12096x^689+40400x^693+42336x^695+41256x^696+61344x^697+19584x^698+52296x^702+40608x^704+36504x^705+49968x^706+14544x^707+624x^711+440x^720+376x^729+184x^738+168x^747+120x^756+40x^765+56x^774+8x^783

The gray image is a linear code over GF(9) with n=783, k=6 and d=657.
This code was found by Heurico 1.16 in 52.2 seconds.