The generator matrix

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

generates a code of length 82 over F9[X]/(X^2) who´s minimum homogenous weight is 637.

Homogenous weight enumerator: w(x)=1x^0+5544x^637+17136x^638+13568x^639+3384x^640+864x^642+23688x^646+57744x^647+34024x^648+5328x^649+3456x^651+39672x^655+78048x^656+41088x^657+7704x^658+7344x^660+47736x^664+92016x^665+46168x^666+6912x^667+16x^702

The gray image is a linear code over GF(9) with n=738, k=6 and d=637.
This code was found by Heurico 1.16 in 42 seconds.