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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+108x^69+222x^72+324x^75+18x^78+18x^81+36x^87+2x^108

The gray image is a linear code over GF(3) with n=111, k=6 and d=69.
This code was found by Heurico 1.16 in 19.8 seconds.