The generator matrix

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

generates a code of length 37 over F9[X]/(X^2) who´s minimum homogenous weight is 279.

Homogenous weight enumerator: w(x)=1x^0+56x^279+1296x^281+864x^282+720x^283+1080x^284+312x^288+9072x^290+3456x^291+1800x^292+1728x^293+184x^297+24624x^299+7344x^300+3312x^301+3024x^302+80x^306+24x^315+40x^324+32x^333

The gray image is a linear code over GF(9) with n=333, k=5 and d=279.
This code was found by Heurico 1.16 in 0.251 seconds.