The generator matrix

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

generates a code of length 39 over Z3[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+168x^74+110x^75+138x^77+66x^78+96x^80+32x^81+42x^83+14x^84+24x^86+6x^87+12x^89+12x^90+6x^92+2x^93

The gray image is a linear code over GF(3) with n=117, k=6 and d=74.
This code was found by Heurico 1.16 in 0.00933 seconds.