The generator matrix
1 1 1 1 1 1 1
0 X^2 0 X^2 0 X^2 2X^2
0 0 X^2 2X^2 2X^2 X^2 0
generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+10x^12+216x^14+12x^15+2x^18+2x^21
The gray image is a linear code over GF(3) with n=63, k=5 and d=36.
This code was found by Heurico 1.16 in 0.000141 seconds.