The generator matrix

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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+96x^106+198x^107+126x^108+444x^109+666x^110+256x^111+876x^112+888x^113+264x^114+1110x^115+1344x^116+334x^117+1458x^118+1506x^119+300x^120+1596x^121+1560x^122+394x^123+1524x^124+1116x^125+170x^126+1008x^127+954x^128+176x^129+444x^130+414x^131+76x^132+186x^133+96x^134+26x^135+6x^136+6x^137+22x^138+16x^141+14x^144+2x^147+6x^150+4x^153

The gray image is a linear code over GF(3) with n=180, k=9 and d=106.
This code was found by Heurico 1.16 in 14.6 seconds.