The generator matrix

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

generates a code of length 76 over Z3[X]/(X^2) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+78x^135+216x^136+432x^137+640x^138+966x^139+924x^140+1324x^141+1608x^142+1530x^143+1788x^144+2316x^145+1974x^146+2510x^147+3000x^148+2562x^149+2958x^150+3264x^151+2514x^152+2880x^153+3498x^154+2604x^155+2746x^156+2844x^157+2196x^158+2474x^159+2124x^160+1530x^161+1392x^162+1266x^163+840x^164+620x^165+570x^166+330x^167+206x^168+168x^169+60x^170+60x^171+30x^172+2x^177+2x^180+2x^186

The gray image is a linear code over GF(3) with n=228, k=10 and d=135.
This code was found by Heurico 1.16 in 61 seconds.