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

generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+214x^114+72x^115+404x^117+138x^118+54x^119+670x^120+204x^121+270x^122+1436x^123+3174x^124+486x^125+2482x^126+6096x^127+432x^128+1836x^129+276x^130+216x^131+426x^132+150x^133+306x^135+84x^136+114x^138+6x^139+64x^141+6x^142+14x^144+24x^147+18x^150+6x^153+2x^159+2x^174

The gray image is a linear code over GF(3) with n=567, k=9 and d=342.
This code was found by Heurico 1.16 in 10.6 seconds.