The generator matrix

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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+156x^135+84x^136+156x^137+554x^138+456x^139+792x^140+1520x^141+1512x^142+2586x^143+3286x^144+2928x^145+6186x^146+5612x^147+3978x^148+8028x^149+6076x^150+3966x^151+4692x^152+2934x^153+1386x^154+786x^155+662x^156+204x^157+90x^158+172x^159+30x^160+12x^161+78x^162+30x^163+32x^165+6x^166+20x^168+12x^171+10x^174+6x^177+4x^180+4x^183+2x^192

The gray image is a linear code over GF(3) with n=666, k=10 and d=405.
This code was found by Heurico 1.16 in 11.7 seconds.