The generator matrix

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

generates a code of length 74 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+78x^144+96x^145+108x^146+202x^147+30x^148+24x^149+50x^150+24x^151+24x^152+54x^153+6x^156+2x^162+6x^164+8x^165+12x^166+4x^168

The gray image is a linear code over GF(3) with n=222, k=6 and d=144.
This code was found by Heurico 1.16 in 0.0716 seconds.