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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+252x^110+234x^111+54x^112+732x^113+408x^114+378x^115+1536x^116+884x^117+1782x^118+3168x^119+750x^120+2862x^121+3072x^122+756x^123+756x^124+726x^125+336x^126+378x^128+150x^129+246x^131+78x^132+60x^134+46x^135+36x^137+2x^153

The gray image is a linear code over GF(3) with n=540, k=9 and d=330.
This code was found by Heurico 1.16 in 1.91 seconds.