The generator matrix

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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+1278x^121+2532x^122+4976x^123+8676x^124+11658x^125+17402x^126+24234x^127+26238x^128+36910x^129+44544x^130+46986x^131+54830x^132+57966x^133+48462x^134+47188x^135+39198x^136+23580x^137+16840x^138+9684x^139+4860x^140+1862x^141+888x^142+342x^143+38x^144+90x^145+78x^146+16x^147+42x^148+18x^149+24x^151

The gray image is a linear code over GF(3) with n=594, k=12 and d=363.
This code was found by Heurico 1.16 in 691 seconds.