The generator matrix

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

generates a code of length 76 over F9[X]/(X^2) who´s minimum homogenous weight is 576.

Homogenous weight enumerator: w(x)=1x^0+512x^576+1192x^585+648x^592+1120x^594+10368x^601+824x^603+41472x^610+808x^612+600x^621+480x^630+360x^639+296x^648+224x^657+112x^666+32x^675

The gray image is a linear code over GF(9) with n=684, k=5 and d=576.
This code was found by Heurico 1.16 in 1.61 seconds.