The generator matrix

 1  0  1  1  1  1 2X^2+X  1  1 2X  1  1  1  0  1  1 2X^2  1  1  1 2X^2+2X  1  1  1  1  1  1  1  0  1  1  1  X  1  1  0  1  1 2X X^2+2X 2X  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X^2+X  1  1 2X^2  1  1  1  1
 0  1  1  2 2X^2+X 2X^2+X+2  1 2X^2+2X+1 2X  1 2X+2 X+1  0  1 2X^2+2  1  1 2X 2X+1 2X^2+2X+2  1 2X^2+2X 2X+2 2X^2+X+1 2X^2 X+1  2 2X^2+2X+1  1  X 2X^2+X+2 2X^2+X  1 2X^2+2X+1 2X^2+2  1 2X^2+1  2  1  1  1 2X+1 2X^2+2X X^2 2X^2+2X+1  0 2X^2+X X^2+2X  2 X+1 X^2+X+2 2X^2+2X+2 2X^2+X+1  1 2X^2+X  1 2X^2+1 X+2  1 X+1 X^2+2X+1 2X+1 2X^2
 0  0 2X  0  0 2X^2 2X^2 2X^2 X^2  0  0 2X^2 X^2+2X 2X^2+2X 2X^2+X 2X^2+X X^2+X 2X  X  X 2X^2+X 2X^2+X 2X 2X^2+X  X 2X X^2+2X X^2+2X 2X 2X^2+X X^2+2X 2X X^2+X X^2 X^2+X 2X^2  0 2X^2 2X  X  0 2X^2+X  X 2X^2+2X 2X  0 2X^2+2X 2X^2 2X X^2+2X X^2+2X  0 2X^2+X X^2+X 2X^2+X 2X^2 2X^2 X^2+X 2X 2X X^2+2X  0  X
 0  0  0 X^2  0  0  0 2X^2  0  0 2X^2 X^2  0  0 2X^2 2X^2 2X^2  0  0 X^2 X^2 X^2 2X^2 2X^2 X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 2X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2  0 X^2 X^2 2X^2  0 2X^2 X^2 2X^2  0 2X^2 2X^2  0 2X^2 X^2 X^2
 0  0  0  0 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2  0 2X^2  0 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2  0  0 2X^2  0  0 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 2X^2 2X^2 2X^2  0 X^2 X^2  0  0  0 2X^2 2X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 2X^2 X^2 X^2 2X^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+144x^115+198x^116+342x^117+774x^118+1308x^119+1958x^120+2694x^121+2880x^122+4058x^123+5544x^124+5004x^125+6150x^126+7560x^127+5196x^128+5562x^129+4278x^130+2328x^131+1498x^132+552x^133+336x^134+52x^135+192x^136+174x^137+30x^138+96x^139+66x^140+4x^141+24x^142+6x^143+14x^144+6x^145+10x^147+6x^148+2x^150+2x^153

The gray image is a linear code over GF(3) with n=567, k=10 and d=345.
This code was found by Heurico 1.16 in 9.73 seconds.