The generator matrix

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

generates a code of length 39 over F9[X]/(X^2) who´s minimum homogenous weight is 306.

Homogenous weight enumerator: w(x)=1x^0+440x^306+2016x^307+360x^308+920x^315+2520x^316+288x^317+16x^324

The gray image is a linear code over GF(9) with n=351, k=4 and d=306.
This code was found by Heurico 1.16 in 0.00849 seconds.