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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+10x^114+36x^115+108x^116+24x^117+258x^118+96x^119+990x^120+480x^121+54x^122+12x^123+18x^124+36x^125+8x^126+12x^127+30x^128+6x^129+6x^130+2x^177

The gray image is a linear code over GF(3) with n=540, k=7 and d=342.
This code was found by Heurico 1.16 in 0.113 seconds.