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

generates a code of length 86 over F9[X]/(X^2) who´s minimum homogenous weight is 668.

Homogenous weight enumerator: w(x)=1x^0+144x^668+1944x^669+14112x^670+28584x^671+1080x^677+8280x^678+43200x^679+76248x^680+400x^684+1944x^686+13896x^687+63720x^688+85752x^689+264x^693+2664x^695+16704x^696+71424x^697+101016x^698+56x^702+8x^711

The gray image is a linear code over GF(9) with n=774, k=6 and d=668.
This code was found by Heurico 1.16 in 76.7 seconds.