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

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+324x^110+168x^111+36x^112+816x^113+606x^114+288x^115+1980x^116+1008x^117+864x^118+3192x^119+1586x^120+1152x^121+3528x^122+1104x^123+576x^124+1068x^125+364x^126+366x^128+186x^129+264x^131+52x^132+102x^134+16x^135+24x^137+4x^138+2x^141+6x^144

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 1.88 seconds.