The generator matrix

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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+252x^139+726x^140+1640x^141+2940x^142+3024x^143+3278x^144+5232x^145+4758x^146+4884x^147+6360x^148+4878x^149+4562x^150+4968x^151+3558x^152+2458x^153+2448x^154+1332x^155+714x^156+606x^157+174x^158+128x^159+18x^160+6x^161+66x^162+6x^163+12x^164+6x^168+12x^169+2x^171

The gray image is a linear code over GF(3) with n=666, k=10 and d=417.
This code was found by Heurico 1.16 in 8.86 seconds.