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

generates a code of length 55 over F9[X]/(X^2) who´s minimum homogenous weight is 420.

Homogenous weight enumerator: w(x)=1x^0+5256x^420+3888x^421+128x^423+216x^424+864x^425+3456x^426+7776x^427+13824x^428+36576x^429+19656x^430+920x^432+3456x^433+6048x^434+13824x^435+20088x^436+22896x^437+65304x^438+31968x^439+5832x^440+5288x^441+13824x^442+16416x^443+29376x^444+36288x^445+39096x^446+91152x^447+37800x^448+88x^450+64x^459+32x^468+24x^477+8x^486+8x^495

The gray image is a linear code over GF(9) with n=495, k=6 and d=420.
This code was found by Heurico 1.16 in 27.3 seconds.