The generator matrix

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

generates a code of length 75 over F9[X]/(X^2) who´s minimum homogenous weight is 567.

Homogenous weight enumerator: w(x)=1x^0+416x^567+432x^572+360x^573+2736x^575+1152x^576+288x^577+576x^578+2736x^579+2520x^580+5904x^581+4176x^582+11376x^584+1088x^585+3024x^586+4752x^587+11232x^588+6048x^589+15984x^590+8640x^591+20736x^593+984x^594+16416x^595+17928x^596+39312x^597+21168x^598+41904x^599+21240x^600+41760x^602+640x^603+32760x^604+29232x^605+51696x^606+22752x^607+40752x^608+18072x^609+28368x^611+696x^612+496x^621+416x^630+320x^639+208x^648+120x^657+8x^666+16x^675

The gray image is a linear code over GF(9) with n=675, k=6 and d=567.
This code was found by Heurico 1.16 in 45.8 seconds.