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

generates a code of length 78 over F9[X]/(X^2) who´s minimum homogenous weight is 605.

Homogenous weight enumerator: w(x)=1x^0+8784x^605+19008x^606+4608x^607+72x^608+432x^610+64x^612+44208x^614+62208x^615+12096x^616+1152x^617+1728x^619+368x^621+66672x^623+86832x^624+13824x^625+4608x^626+3672x^628+280x^630+84456x^632+100224x^633+16128x^634+8x^666+8x^684

The gray image is a linear code over GF(9) with n=702, k=6 and d=605.
This code was found by Heurico 1.16 in 39.4 seconds.