The generator matrix

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

generates a code of length 89 over F9[X]/(X^2) who´s minimum homogenous weight is 688.

Homogenous weight enumerator: w(x)=1x^0+2664x^688+360x^691+2232x^692+1920x^693+2448x^694+7776x^695+15048x^696+20448x^697+2160x^699+4824x^700+10512x^701+10456x^702+10224x^703+21096x^704+31752x^705+37080x^706+5400x^708+8712x^709+17640x^710+15808x^711+13032x^712+25200x^713+33912x^714+40464x^715+9936x^717+15264x^718+27936x^719+18992x^720+15120x^721+27576x^722+35928x^723+39312x^724+64x^729+80x^738+40x^747+24x^756

The gray image is a linear code over GF(9) with n=801, k=6 and d=688.
This code was found by Heurico 1.16 in 46.6 seconds.