The generator matrix

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

generates a code of length 44 over F9[X]/(X^2) who´s minimum homogenous weight is 332.

Homogenous weight enumerator: w(x)=1x^0+3384x^332+176x^333+648x^336+2520x^337+6768x^338+13392x^339+12528x^340+23832x^341+96x^342+648x^344+10368x^345+18288x^346+27936x^347+34776x^348+21600x^349+41976x^350+152x^351+5184x^353+41472x^354+49176x^355+58608x^356+62640x^357+35856x^358+59112x^359+128x^360+96x^369+72x^378+8x^387

The gray image is a linear code over GF(9) with n=396, k=6 and d=332.
This code was found by Heurico 1.16 in 21.4 seconds.