The generator matrix

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

generates a code of length 76 over Z3[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+90x^138+156x^139+294x^140+610x^141+582x^142+714x^143+1060x^144+696x^145+714x^146+1002x^147+762x^148+858x^149+1164x^150+912x^151+846x^152+1158x^153+900x^154+774x^155+1068x^156+738x^157+714x^158+830x^159+540x^160+480x^161+518x^162+306x^163+258x^164+318x^165+198x^166+150x^167+148x^168+36x^169+30x^170+44x^171+6x^172+6x^174+2x^177

The gray image is a linear code over GF(3) with n=228, k=9 and d=138.
This code was found by Heurico 1.16 in 7.34 seconds.