The generator matrix

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

generates a code of length 39 over F9[X]/(X^2) who´s minimum homogenous weight is 291.

Homogenous weight enumerator: w(x)=1x^0+1224x^291+648x^296+3184x^297+4320x^298+23760x^299+17928x^300+3240x^304+10368x^305+21432x^306+17280x^307+59400x^308+38232x^309+25920x^313+41472x^314+57536x^315+36720x^316+109296x^317+59256x^318+112x^324+72x^333+40x^342

The gray image is a linear code over GF(9) with n=351, k=6 and d=291.
This code was found by Heurico 1.16 in 18.1 seconds.