The generator matrix

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

generates a code of length 87 over F9[X]/(X^2) who´s minimum homogenous weight is 672.

Homogenous weight enumerator: w(x)=1x^0+2376x^672+144x^674+376x^675+1080x^676+2880x^677+4320x^678+9360x^679+13536x^680+17208x^681+3816x^683+2656x^684+6048x^685+16344x^686+15120x^687+21888x^688+25272x^689+29376x^690+11376x^692+6096x^693+11880x^694+26064x^695+20952x^696+25344x^697+30024x^698+35640x^699+19656x^701+8872x^702+15984x^703+30528x^704+23760x^705+30888x^706+30312x^707+32040x^708+104x^711+48x^720+24x^729+48x^738

The gray image is a linear code over GF(9) with n=783, k=6 and d=672.
This code was found by Heurico 1.16 in 45.9 seconds.