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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+102x^116+66x^117+108x^118+108x^119+1578x^120+54x^122+42x^123+54x^124+24x^125+12x^126+36x^128+2x^180

The gray image is a linear code over GF(3) with n=540, k=7 and d=348.
This code was found by Heurico 1.16 in 0.0884 seconds.