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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+1446x^123+2772x^124+4584x^125+9280x^126+12870x^127+14910x^128+24156x^129+29844x^130+32658x^131+44606x^132+54060x^133+48060x^134+56212x^135+55062x^136+41334x^137+38216x^138+27018x^139+14484x^140+11360x^141+4902x^142+1806x^143+942x^144+486x^145+72x^146+112x^147+54x^148+36x^149+50x^150+42x^151+6x^155

The gray image is a linear code over GF(3) with n=603, k=12 and d=369.
This code was found by Heurico 1.16 in 828 seconds.