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

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+80x^111+54x^112+268x^114+126x^115+216x^116+234x^117+96x^118+864x^119+3116x^120+60x^121+864x^122+150x^123+60x^124+114x^126+12x^127+76x^129+48x^130+48x^132+30x^133+38x^135+2x^138+2x^141+2x^174

The gray image is a linear code over GF(3) with n=540, k=8 and d=333.
This code was found by Heurico 1.16 in 0.321 seconds.