The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 X 1 0 1 1 1 1 1 1 0 1 1 0 1 2X 1 1 1 1 1 1 0 1 1 0 X 2X 1 1 1 1 1 1 1 1 1 1 1 2X 1 1 X 1 1 2X X 0 1 1 1 X 1 X 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 2 1 0 1 0 2X+1 2 2 X 2X+1 1 X 2X+1 1 2 1 X+2 2X+1 2X+2 0 2X+1 2 1 X 0 1 1 1 X+1 X+1 X 1 2 0 2X+2 X 2X 2X+1 0 1 2X 2X+2 1 2X+1 X+1 1 1 1 2X+1 0 0 1 X+2 0 2X+1
0 0 2X 0 0 0 0 0 0 2X X X 2X X X 2X 0 2X X 2X 0 0 2X 0 X X 2X 2X 0 2X X 0 0 2X 0 2X X 2X X 2X X X X 2X 0 X X 2X 2X 0 X 2X 2X 2X X X X X 2X X 2X X 0 2X 2X X X 2X
0 0 0 X 0 0 0 0 0 0 0 2X 2X X 2X 2X 2X X 0 2X 2X 2X 2X 2X 0 X 0 X 0 X 2X 2X 2X 2X 2X 0 0 2X X X 2X 2X 0 2X 2X 0 0 0 2X 0 0 0 2X X 2X 0 0 2X 0 X X X 2X X X X X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X X X X X 2X 2X X 2X X 2X X X X 2X X 2X X 0 X 2X 2X 0 2X 2X 2X 2X 0 0 0 X 2X 2X X X 2X X X 0 0 X 2X X 0 2X 0
0 0 0 0 0 2X 0 0 0 0 0 0 0 0 0 X X X 2X X 2X 0 2X 2X 2X 2X X 0 2X X 0 2X X X X 2X 0 0 X 2X X X X 0 2X 2X X 2X 0 2X X 2X 0 0 2X 0 X X X X X 2X 0 2X X 2X X 2X
0 0 0 0 0 0 X 0 2X 2X X 2X 2X 2X 2X 2X 0 0 0 X X X 2X X X 0 2X X 2X 0 X 2X 2X X X X 0 X 0 0 2X 0 0 0 2X 2X 2X 0 2X 2X 0 X 2X 0 0 X 0 0 X 2X 0 X 2X 0 X 0 2X 0
0 0 0 0 0 0 0 X X 2X 0 2X X 0 X 0 2X X 2X X 0 X 2X 0 2X 0 2X 0 2X X 2X X 2X 2X X X 2X 0 0 2X X X 0 X X 0 2X 0 0 X 2X 2X 0 X 0 2X 2X 0 2X 0 0 0 X X 0 2X 2X 0
generates a code of length 68 over Z3[X]/(X^2) who´s minimum homogenous weight is 114.
Homogenous weight enumerator: w(x)=1x^0+114x^114+18x^116+296x^117+42x^118+150x^119+366x^120+288x^121+468x^122+442x^123+738x^124+1122x^125+524x^126+1638x^127+2244x^128+544x^129+2832x^130+3324x^131+560x^132+4440x^133+4584x^134+540x^135+5436x^136+5052x^137+626x^138+5100x^139+4206x^140+530x^141+3342x^142+3054x^143+508x^144+1776x^145+1464x^146+498x^147+528x^148+426x^149+350x^150+66x^151+132x^152+268x^153+18x^154+212x^156+100x^159+50x^162+22x^165+10x^168
The gray image is a linear code over GF(3) with n=204, k=10 and d=114.
This code was found by Heurico 1.16 in 60.3 seconds.