The generator matrix

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

generates a code of length 68 over Z3[X]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+198x^120+216x^121+534x^122+918x^123+864x^124+1068x^125+1746x^126+1464x^127+1596x^128+2494x^129+2022x^130+2070x^131+3400x^132+2634x^133+2832x^134+3660x^135+2904x^136+2766x^137+4044x^138+2778x^139+2772x^140+3346x^141+2292x^142+2094x^143+2290x^144+1338x^145+1254x^146+1314x^147+708x^148+402x^149+456x^150+258x^151+108x^152+142x^153+18x^154+32x^156+14x^159+2x^168

The gray image is a linear code over GF(3) with n=204, k=10 and d=120.
This code was found by Heurico 1.16 in 67.6 seconds.