The generator matrix

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

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+48x^69+162x^70+78x^72+96x^73+54x^75+162x^76+36x^78+36x^79+18x^81+30x^82+6x^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 0.00937 seconds.