The generator matrix
1 0 1 1 1
0 1 1 a a^7*X+a^2
0 0 a^7*X a*X a^6*X
generates a code of length 5 over F9[X]/(X^2) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+80x^27+3240x^32+240x^36+29160x^40+25920x^41+408x^45
The gray image is a linear code over GF(9) with n=45, k=5 and d=27.
This code was found by Heurico 1.16 in 0.0122 seconds.