The generator matrix

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

generates a code of length 42 over F9[X]/(X^2) who´s minimum homogenous weight is 306.

Homogenous weight enumerator: w(x)=1x^0+320x^306+360x^307+216x^312+288x^313+720x^314+2504x^315+4032x^316+1296x^320+5184x^321+3024x^322+4320x^323+6720x^324+12960x^325+20736x^329+41472x^330+16416x^331+18360x^332+20696x^333+42192x^334+82944x^338+110592x^339+32760x^340+29088x^341+26800x^342+45432x^343+896x^351+704x^360+336x^369+72x^378

The gray image is a linear code over GF(9) with n=378, k=6 and d=306.
This code was found by Heurico 1.16 in 22.7 seconds.