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

generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+318x^116+234x^117+570x^119+510x^120+1284x^122+1010x^123+1458x^124+2736x^125+3140x^126+2916x^127+2592x^128+1116x^129+546x^131+254x^132+354x^134+146x^135+204x^137+82x^138+132x^140+48x^141+12x^143+16x^144+2x^150+2x^174

The gray image is a linear code over GF(3) with n=567, k=9 and d=348.
This code was found by Heurico 1.16 in 2.1 seconds.