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

generates a code of length 41 over F9[X]/(X^2) who´s minimum homogenous weight is 307.

Homogenous weight enumerator: w(x)=1x^0+2016x^307+288x^312+2592x^313+4320x^314+23968x^315+22032x^316+3240x^320+4608x^321+18144x^322+17280x^323+59664x^324+50976x^325+5832x^328+25920x^329+18432x^330+49248x^331+36720x^332+109376x^333+76608x^334+96x^342+32x^351+40x^360+8x^369

The gray image is a linear code over GF(9) with n=369, k=6 and d=307.
This code was found by Heurico 1.16 in 19.7 seconds.