The generator matrix

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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+162x^115+312x^116+38x^117+366x^118+426x^119+384x^120+606x^121+2052x^122+738x^123+558x^124+414x^125+40x^126+120x^127+72x^128+12x^129+36x^130+30x^131+54x^133+84x^134+36x^136+6x^137+6x^139+6x^140+2x^171

The gray image is a linear code over GF(3) with n=549, k=8 and d=345.
This code was found by Heurico 1.16 in 2.82 seconds.