The generator matrix

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

generates a code of length 74 over Z3[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+338x^138+114x^139+210x^140+518x^141+300x^142+288x^143+760x^144+276x^145+294x^146+554x^147+288x^148+240x^149+394x^150+162x^151+156x^152+366x^153+120x^154+84x^155+298x^156+66x^157+102x^158+156x^159+60x^160+42x^161+160x^162+54x^163+36x^164+70x^165+18x^166+6x^167+30x^168

The gray image is a linear code over GF(3) with n=222, k=8 and d=138.
This code was found by Heurico 1.16 in 200 seconds.