The generator matrix

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

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+44x^69+48x^70+186x^71+82x^72+60x^73+42x^74+46x^75+24x^76+36x^77+34x^78+18x^79+42x^80+32x^81+6x^82+6x^83+2x^84+6x^85+12x^86+2x^90

The gray image is a linear code over GF(3) with n=111, k=6 and d=69.
This code was found by Heurico 1.13 in 0.0541 seconds.