The generator matrix

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

generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+1260x^115+1860x^116+4812x^117+7848x^118+10920x^119+17586x^120+22476x^121+27324x^122+37416x^123+43476x^124+49758x^125+57872x^126+57366x^127+50862x^128+47902x^129+36564x^130+23952x^131+16068x^132+8922x^133+3750x^134+2196x^135+792x^136+138x^137+62x^138+108x^139+78x^140+24x^141+36x^142+12x^144

The gray image is a linear code over GF(3) with n=567, k=12 and d=345.
This code was found by Heurico 1.16 in 526 seconds.