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  X  1  1  1  X  1  1  1  0  1  X  1  1  1  1  1  X  1  X  0  1  1  1  X  1  1  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X X^2 2X^2+X 2X X^2+2X  0 2X^2+X X^2+X X^2+2X X^2 2X  0 2X^2+X X^2+X  X  0 2X X^2+2X 2X^2 X^2+2X X^2+2X X^2  X 2X^2+2X X^2+X 2X^2+X 2X^2+X 2X^2 2X^2+X 2X X^2+2X  0 X^2  X X^2 2X^2+X  0 X^2+2X 2X^2+X 2X  X 2X X^2+X 2X^2+X  X 2X^2 2X^2+2X 2X^2+X 2X 2X^2+2X  X X^2+2X
 0  0 X^2  0  0  0  0 2X^2 X^2  0 X^2 2X^2 2X^2  0  0 X^2  0  0 X^2 2X^2 2X^2 X^2 X^2 2X^2  0 2X^2 X^2 2X^2 X^2 X^2  0 X^2 X^2 2X^2 2X^2 X^2  0 2X^2 X^2 X^2  0 X^2 2X^2 2X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 2X^2  0 X^2 2X^2 2X^2  0
 0  0  0 X^2  0  0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2  0 X^2 X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2  0  0  0  0 2X^2  0  0 X^2  0 X^2 2X^2  0  0 2X^2 X^2  0 X^2  0 2X^2  0  0 2X^2 2X^2
 0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2  0 X^2 2X^2  0 2X^2  0 2X^2  0 2X^2 2X^2  0  0  0 X^2  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2 2X^2  0  0 X^2 2X^2 2X^2 X^2  0 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 X^2  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2
 0  0  0  0  0 X^2 X^2  0 2X^2 X^2  0  0 X^2 X^2 2X^2 2X^2 X^2 X^2  0 2X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 2X^2 2X^2 X^2 X^2  0 X^2 X^2 2X^2  0 2X^2  0 X^2 2X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 2X^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+54x^109+24x^110+384x^111+192x^112+120x^113+802x^114+168x^115+732x^116+2476x^117+240x^118+2304x^119+4452x^120+288x^121+2364x^122+3164x^123+246x^124+240x^125+450x^126+192x^127+48x^128+304x^129+60x^130+96x^132+18x^133+32x^135+16x^138+20x^141+8x^144+4x^147+4x^150+6x^156

The gray image is a linear code over GF(3) with n=540, k=9 and d=324.
This code was found by Heurico 1.16 in 2.7 seconds.