The generator matrix

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

generates a code of length 46 over F9[X]/(X^2) who´s minimum homogenous weight is 348.

Homogenous weight enumerator: w(x)=1x^0+4464x^348+216x^351+720x^352+2808x^353+4104x^354+9864x^355+17712x^356+28224x^357+136x^360+11520x^361+19656x^362+17712x^363+25632x^364+30672x^365+52632x^366+112x^369+46080x^370+53352x^371+36504x^372+46152x^373+50760x^374+72144x^375+80x^378+104x^387+80x^396

The gray image is a linear code over GF(9) with n=414, k=6 and d=348.
This code was found by Heurico 1.16 in 23.7 seconds.