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  1  1  X  1  1  X  1  X  1
 0  X  0  0  0  0  X 2X 2X  0  0  X  X  X  X  X  X  X  0 2X  0 2X  0 2X 2X 2X 2X 2X  0  X 2X  0  X 2X  X 2X
 0  0  X  0  0  X 2X  0 2X  0  X  X 2X 2X  0  X  0  X  X  X  X  0  0  X 2X 2X  X 2X  X  X  X  0  0  0 2X  0
 0  0  0  X  0 2X 2X  X  0  X  X  0  0  X 2X  X  X 2X 2X  0  X  0  0 2X 2X 2X 2X  X  0  0  X  X  0 2X  0 2X
 0  0  0  0  X 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  X  0  0  X 2X 2X 2X  0  X  X 2X  X  X  0  X  0  0  X  X

generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+88x^66+174x^69+256x^72+148x^75+24x^78+8x^81+16x^84+12x^90+2x^99

The gray image is a linear code over GF(3) with n=108, k=6 and d=66.
This code was found by Heurico 1.16 in 33.1 seconds.