The generator matrix

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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+174x^108+48x^109+138x^110+608x^111+648x^112+732x^113+1572x^114+2898x^115+2346x^116+3128x^117+7752x^118+4608x^119+5318x^120+10422x^121+4626x^122+4124x^123+5472x^124+1974x^125+1250x^126+408x^127+114x^128+416x^129+54x^130+42x^131+70x^132+44x^135+24x^138+10x^141+16x^144+6x^147+2x^150+4x^153

The gray image is a linear code over GF(3) with n=540, k=10 and d=324.
This code was found by Heurico 1.16 in 16.3 seconds.