The generator matrix

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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+772x^114+1008x^115+1638x^116+3792x^117+4014x^118+3744x^119+6642x^120+5256x^121+5112x^122+6454x^123+5526x^124+4140x^125+4644x^126+2628x^127+1332x^128+1476x^129+522x^130+72x^131+172x^132+68x^135+36x^138

The gray image is a linear code over GF(3) with n=549, k=10 and d=342.
This code was found by Heurico 1.16 in 6.93 seconds.