The generator matrix

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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+154x^111+252x^112+252x^113+894x^114+918x^115+612x^116+1604x^117+1854x^118+1512x^119+2582x^120+2448x^121+1422x^122+2082x^123+1620x^124+576x^125+478x^126+198x^127+134x^129+46x^132+24x^135+8x^138+2x^141+6x^144+2x^147+2x^153

The gray image is a linear code over GF(3) with n=540, k=9 and d=333.
This code was found by Heurico 1.16 in 1.13 seconds.