The generator matrix

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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+270x^110+182x^111+588x^113+466x^114+822x^116+358x^117+840x^119+386x^120+624x^122+252x^123+516x^125+228x^126+390x^128+174x^129+192x^131+90x^132+120x^134+32x^135+12x^137+10x^138+2x^141+2x^144+4x^147

The gray image is a linear code over GF(3) with n=180, k=8 and d=110.
This code was found by Heurico 1.16 in 0.606 seconds.