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 X 1 1 1 X^2 X^2 0 X X X 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 0 X^2 2X^2 0 0 X^2 2X^2 X^2 2X^2 X^2 0 X^2 0 0
generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.
Homogenous weight enumerator: w(x)=1x^0+56x^102+6x^104+4x^105+12x^107+2x^111
The gray image is a linear code over GF(3) with n=459, k=4 and d=306.
This code was found by Heurico 1.16 in 0.034 seconds.