The generator matrix

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

generates a code of length 61 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+170x^105+90x^106+336x^107+470x^108+402x^109+1020x^110+1110x^111+810x^112+1734x^113+1638x^114+1176x^115+2958x^116+2562x^117+1896x^118+4284x^119+3002x^120+2328x^121+4878x^122+3594x^123+2562x^124+4776x^125+3228x^126+1914x^127+3384x^128+2048x^129+1230x^130+2016x^131+1056x^132+546x^133+732x^134+470x^135+162x^136+114x^137+188x^138+6x^139+12x^140+62x^141+44x^144+24x^147+14x^150+2x^153

The gray image is a linear code over GF(3) with n=183, k=10 and d=105.
This code was found by Heurico 1.16 in 60.4 seconds.