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

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+136x^114+276x^115+216x^116+392x^117+792x^118+300x^119+988x^120+1506x^121+1242x^122+2092x^123+3648x^124+2046x^125+2218x^126+1830x^127+294x^128+330x^129+276x^130+150x^131+204x^132+216x^133+78x^134+116x^135+150x^136+36x^137+66x^138+36x^139+12x^140+16x^141+18x^142+2x^165

The gray image is a linear code over GF(3) with n=558, k=9 and d=342.
This code was found by Heurico 1.16 in 1.91 seconds.