The generator matrix

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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+426x^114+180x^115+468x^116+2002x^117+1548x^118+1854x^119+4242x^120+3726x^121+4914x^122+6300x^123+5922x^124+6390x^125+6710x^126+4878x^127+3546x^128+3098x^129+1242x^130+324x^131+734x^132+326x^135+164x^138+44x^141+2x^144+2x^147+2x^150+4x^153

The gray image is a linear code over GF(3) with n=558, k=10 and d=342.
This code was found by Heurico 1.16 in 13 seconds.