The generator matrix

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

generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+1198x^138+1350x^139+1872x^140+4184x^141+3978x^142+3654x^143+6362x^144+5148x^145+3978x^146+7006x^147+4860x^148+3096x^149+4364x^150+2718x^151+1638x^152+1892x^153+900x^154+342x^155+370x^156+92x^159+34x^162+12x^165

The gray image is a linear code over GF(3) with n=657, k=10 and d=414.
This code was found by Heurico 1.16 in 19.7 seconds.