The generator matrix
1 0 1 1 1 1 1 0 1 1 1 X 1 1 1 X 1 1 1 1 1 1 0 X 1 1 1 1 1 1 1 1 2X 1
0 1 1 2 2X+1 0 2 1 X 2X+1 X+2 1 X X+1 X+2 1 X+1 0 X 1 2 X+2 1 1 2X 2X 2X 2X+1 X+1 1 2X+2 2X+2 1 0
0 0 2X 0 X X 2X 2X 2X 0 X X X 2X 2X 2X X 2X 0 0 X 0 X 0 0 X 2X 2X 0 X 0 X 0 2X
generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.
Homogenous weight enumerator: w(x)=1x^0+52x^66+36x^67+54x^68+64x^69+18x^70+12x^72+2x^75+2x^78+2x^81
The gray image is a linear code over GF(3) with n=102, k=5 and d=66.
This code was found by Heurico 1.16 in 0.00508 seconds.