The generator matrix

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

generates a code of length 39 over Z3[X]/(X^2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+54x^73+60x^74+240x^75+36x^76+48x^77+30x^78+24x^79+16x^81+18x^82+48x^83+112x^84+18x^85+6x^86+12x^88+4x^90+2x^93

The gray image is a linear code over GF(3) with n=117, k=6 and d=73.
This code was found by Heurico 1.16 in 0.126 seconds.