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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+240x^113+170x^114+438x^116+248x^117+972x^118+186x^119+1362x^120+1944x^121+222x^122+290x^123+150x^125+70x^126+78x^128+24x^129+78x^131+8x^132+60x^134+12x^135+6x^137+2x^171

The gray image is a linear code over GF(3) with n=540, k=8 and d=339.
This code was found by Heurico 1.16 in 1.52 seconds.