The generator matrix

 1  0  1  1  1  1  1  X 2X  1  1  1  1 2X^2  1  1  X  1  1  1  1  1  1  1 2X^2+2X  1  1  1  1  1  0 2X^2+2X  1  1  1  1 X^2 2X  1  1  1  1  0  1 2X^2+2X  1  1  1  0  1 X^2 2X^2+2X  1  1  1  1  1 2X^2+X  0 2X^2  X X^2+X  1
 0  1  1  2 2X^2 2X+1  2  1  1  2 2X^2+2X+1 2X^2+X X+1  1 2X^2 X+2  1 X^2+2X X^2+2X+2 2X^2+X+1 2X^2 X+2 X^2+X+1 2X^2+2X  1 2X^2+1 2X^2+X+2  X X+2 2X^2+X+1  1  1 X+1 X^2+2X 2X^2+2X+1 2X^2+X  1  1 2X  0 2X^2+1 2X^2+2  1 X^2+2X+1  1 2X+2 X^2+2 X^2+X+2  1 2X^2+X+2  1  1 2X^2  X 2X^2+X+1 2X 2X  1  1  1 X^2  1  1
 0  0 2X  0 2X^2  0  0 X^2  0 2X^2 2X^2 X^2 X^2 X^2+X  X 2X^2+2X 2X 2X X^2+X X^2+X 2X^2+X 2X^2+X 2X 2X X^2+2X X^2+X X^2+X 2X^2+2X X^2+2X 2X  X X^2+X X^2 X^2 X^2+2X X^2+X 2X X^2+2X 2X^2+X X^2 X^2  X X^2+2X X^2+X  X 2X^2+2X  X  0  X X^2+2X X^2 X^2+2X  X 2X X^2  0 X^2+2X X^2+2X X^2+X X^2+2X  X  X X^2+X
 0  0  0  X 2X^2+X X^2+X X^2  X X^2+2X X^2+2X 2X^2+2X 2X 2X^2 X^2+2X X^2 X^2+X 2X 2X^2+X 2X^2+2X X^2 2X^2+2X 2X^2  X 2X^2  0 2X  X X^2+2X X^2 2X^2+2X  X 2X^2 2X^2+2X X^2+2X 2X^2 X^2+X X^2  X 2X X^2 2X^2 2X^2+2X 2X  X X^2+2X X^2+X 2X^2+X  0 2X^2 2X^2+2X X^2+X X^2 X^2+X X^2+X X^2  X 2X  0 X^2 X^2+X  0 X^2+2X  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+252x^116+362x^117+468x^118+1596x^119+2136x^120+2214x^121+3498x^122+4332x^123+4788x^124+5898x^125+6910x^126+5850x^127+5580x^128+5642x^129+3564x^130+2634x^131+1410x^132+612x^133+582x^134+192x^135+240x^137+104x^138+96x^140+36x^141+36x^143+14x^144+2x^147

The gray image is a linear code over GF(3) with n=567, k=10 and d=348.
This code was found by Heurico 1.16 in 9.11 seconds.