The generator matrix

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

generates a code of length 69 over F9[X]/(X^2) who´s minimum homogenous weight is 513.

Homogenous weight enumerator: w(x)=1x^0+56x^513+216x^517+696x^522+72x^523+144x^524+2304x^526+1440x^530+6712x^531+2160x^532+3168x^533+9576x^535+8640x^539+23240x^540+6696x^541+7776x^542+18792x^544+36720x^548+79792x^549+20664x^550+21024x^551+40032x^553+58176x^557+104000x^558+22896x^559+20376x^560+34056x^562+520x^567+576x^576+440x^585+256x^594+176x^603+40x^612+8x^621

The gray image is a linear code over GF(9) with n=621, k=6 and d=513.
This code was found by Heurico 1.16 in 40.2 seconds.