The generator matrix
1 0 1 1 1 1 1 0 1 1 1 X 1 1 1 X 1 1 1 1 X 0 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 2 X 1 1
0 0 2X 0 X X 2X 2X 2X 0 X X X 2X 2X 2X X 2X 0 X X X 0
generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 43.
Homogenous weight enumerator: w(x)=1x^0+36x^43+60x^44+8x^45+48x^46+36x^47+12x^48+12x^49+6x^51+12x^52+12x^53
The gray image is a linear code over GF(3) with n=69, k=5 and d=43.
This code was found by Heurico 1.16 in 0.00137 seconds.