The generator matrix
1 0 1 1 1 1 1 1
0 1 a^7*X+1 a a^7*X+a^2 a^3 a^7*X+2 a^5
generates a code of length 8 over F9[X]/(X^2) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+576x^56+64x^63+1296x^64+4608x^65+16x^72
The gray image is a linear code over GF(9) with n=72, k=4 and d=56.
This code was found by Heurico 1.16 in 0.000455 seconds.