The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+132x^70+162x^71+32x^72+66x^73+84x^74+24x^75+48x^76+48x^77+22x^78+48x^79+24x^82+6x^83+6x^85+24x^86+2x^87

The gray image is a linear code over GF(3) with n=111, k=6 and d=70.
This code was found by Heurico 1.16 in 3.23 seconds.