The generator matrix

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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+1308x^119+2134x^120+4878x^121+8892x^122+11538x^123+17406x^124+22002x^125+27074x^126+38628x^127+44376x^128+45936x^129+57474x^130+56430x^131+50574x^132+47556x^133+37182x^134+23944x^135+17154x^136+9252x^137+3912x^138+2070x^139+1170x^140+312x^141+90x^143+38x^144+72x^146+20x^147+18x^149

The gray image is a linear code over GF(3) with n=585, k=12 and d=357.
This code was found by Heurico 1.16 in 526 seconds.