The generator matrix

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

generates a code of length 13 over F9[X]/(X^2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+432x^89+136x^90+4536x^96+3024x^98+216x^99+5832x^104+36288x^105+8208x^107+200x^108+176x^117

The gray image is a linear code over GF(9) with n=117, k=5 and d=89.
This code was found by Heurico 1.16 in 0.343 seconds.