The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 X X 1 1 1 X X X 1 X^2 X^2 0 X X X X 1 1
0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 X^2 2X^2 0 X^2 2X^2 X^2 2X^2 0 X^2 2X^2 X^2 2X^2 0 0 X^2 2X^2 X^2 0 X^2 2X^2 0 X^2 0
generates a code of length 50 over Z3[X]/(X^3) who´s minimum homogenous weight is 100.
Homogenous weight enumerator: w(x)=1x^0+54x^100+14x^102+8x^105+4x^108
The gray image is a linear code over GF(3) with n=450, k=4 and d=300.
This code was found by Heurico 1.16 in 0.0316 seconds.