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
0 X 0 X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 X X
0 0 X 2X 2X X 0 X 2X 0 X 2X X 2X 0 0 X 2X 0 X 2X X
generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+12x^42+54x^44+8x^45+4x^48+2x^66
The gray image is a linear code over GF(3) with n=66, k=4 and d=42.
This code was found by Heurico 1.16 in 0.00118 seconds.