The generator matrix

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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+486x^137+776x^138+2148x^139+3060x^140+4416x^141+6414x^142+8826x^143+9362x^144+11202x^145+15042x^146+13962x^147+17394x^148+19266x^149+15216x^150+15102x^151+12450x^152+8382x^153+6042x^154+3774x^155+1746x^156+804x^157+576x^158+248x^159+96x^160+114x^161+60x^162+72x^163+30x^164+16x^165+6x^166+30x^167+4x^168+6x^169+12x^170+6x^175

The gray image is a linear code over GF(3) with n=666, k=11 and d=411.
This code was found by Heurico 1.16 in 78.4 seconds.