The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+342x^101+392x^102+402x^103+1110x^104+956x^105+834x^106+1992x^107+1776x^108+1344x^109+2808x^110+2574x^111+1962x^112+4236x^113+3202x^114+2142x^115+4656x^116+3832x^117+2382x^118+4446x^119+3168x^120+2172x^121+3642x^122+2278x^123+1272x^124+1974x^125+1024x^126+486x^127+882x^128+366x^129+108x^130+138x^131+68x^132+18x^133+18x^134+12x^135+14x^138+12x^141+6x^144+2x^147

The gray image is a linear code over GF(3) with n=174, k=10 and d=101.
This code was found by Heurico 1.16 in 48.6 seconds.