The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1
0 X 0 0 X 0 X X 2X 0 0 X X 0 2X X 2X 2X X 0 X 0
0 0 X 0 2X X 2X X 2X 0 X X 0 2X 0 0 X X X 2X 2X 0
0 0 0 X 2X 2X 0 2X 2X 2X X 0 2X 0 2X X X 0 X X X 0
generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.
Homogenous weight enumerator: w(x)=1x^0+12x^39+84x^42+128x^45+6x^48+6x^51+4x^54+2x^63
The gray image is a linear code over GF(3) with n=66, k=5 and d=39.
This code was found by Heurico 1.16 in 0.00194 seconds.