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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+108x^115+46x^117+306x^118+100x^120+306x^121+486x^122+272x^123+3174x^124+972x^125+250x^126+162x^127+22x^129+108x^130+14x^132+60x^133+14x^135+72x^136+4x^138+72x^139+2x^141+6x^142+2x^144+2x^180

The gray image is a linear code over GF(3) with n=558, k=8 and d=345.
This code was found by Heurico 1.16 in 0.34 seconds.