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

generates a code of length 56 over F9[X]/(X^2) who´s minimum homogenous weight is 428.

Homogenous weight enumerator: w(x)=1x^0+4248x^428+5832x^429+408x^432+648x^433+3888x^434+2808x^435+20880x^436+26928x^437+29304x^438+1296x^440+3656x^441+4536x^442+15552x^443+7344x^444+36000x^445+46800x^446+48312x^447+5832x^448+10368x^449+13984x^450+12312x^451+33048x^452+13176x^453+59760x^454+67824x^455+56520x^456+32x^459+72x^468+24x^477+24x^486+16x^495+8x^504

The gray image is a linear code over GF(9) with n=504, k=6 and d=428.
This code was found by Heurico 1.16 in 27.7 seconds.