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

generates a code of length 59 over Z3[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+150x^110+148x^111+354x^113+150x^114+240x^116+116x^117+252x^119+120x^120+192x^122+96x^123+120x^125+46x^126+120x^128+32x^129+30x^131+2x^132+6x^135+4x^138+2x^141+2x^144+2x^147+2x^150

The gray image is a linear code over GF(3) with n=177, k=7 and d=110.
This code was found by Heurico 1.16 in 0.389 seconds.