The generator matrix

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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+174x^112+246x^114+246x^115+170x^117+300x^118+258x^121+158x^123+222x^124+68x^126+186x^127+54x^130+64x^132+18x^133+4x^135+16x^141+2x^150

The gray image is a linear code over GF(3) with n=180, k=7 and d=112.
This code was found by Heurico 1.16 in 81.8 seconds.