The generator matrix

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

generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+110x^135+168x^136+546x^137+1070x^138+1584x^139+1692x^140+2718x^141+3270x^142+3816x^143+5454x^144+5220x^145+5490x^146+6688x^147+5958x^148+4740x^149+4438x^150+2598x^151+1320x^152+798x^153+462x^154+204x^155+166x^156+66x^157+78x^158+102x^159+72x^160+60x^161+60x^162+36x^163+24x^164+18x^165+6x^166+6x^167+2x^168+6x^170+2x^174

The gray image is a linear code over GF(3) with n=657, k=10 and d=405.
This code was found by Heurico 1.16 in 10.7 seconds.