The generator matrix

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

generates a code of length 52 over F9[X]/(X^2) who´s minimum homogenous weight is 396.

Homogenous weight enumerator: w(x)=1x^0+3880x^396+4896x^397+504x^400+1656x^401+3312x^402+6336x^403+13536x^404+29592x^405+20016x^406+1296x^408+8064x^409+12240x^410+14112x^411+16488x^412+23472x^413+52592x^414+33408x^415+10368x^417+32256x^418+32760x^419+29232x^420+29664x^421+38808x^422+71928x^423+40824x^424+64x^432+64x^441+56x^450+16x^459

The gray image is a linear code over GF(9) with n=468, k=6 and d=396.
This code was found by Heurico 1.16 in 24.7 seconds.