The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 0 1 1 1 1 0 1 X 1 1 1 1 1 1 2X 1 1 1 1 X 1 1 1 1 1 1 1 1 1 0 1 1 1 1 2X 1 X 1 1 1 1 0 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 2 1 1 2X+1 2 0 X+2 1 0 2X+1 2 X+1 1 0 1 2X+1 2 X+2 2X+1 X X 1 X X+2 2X+2 1 1 2X 1 2X+2 0 2X X 1 2X 2 1 2X 2X+1 0 1 1 2X+1 1 2X+1 X+2 X+2 X+2 1 2X+2 0 2X+2 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X 2X X 2X 2X X 2X X X 0 2X X 0 2X 0 2X 2X 0 2X X X X 0 2X X X 0 2X X 2X 0 X 0 X X 2X 2X 2X 2X X X 2X 2X 0 X 2X X 0 X 2X X 2X 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 2X 2X 2X X 2X 0 2X 0 X 2X 2X X X 2X X 0 0 0 X 2X 2X 2X 0 0 2X 0 2X X 2X X 2X X X X 0 0 X 2X 0 2X X X 2X 0 X 0 2X 2X X 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X X 0 0 X 2X 2X 0 0 X 0 2X 2X 2X X 0 X X 0 2X X 0 X X 2X 0 0 2X 2X 2X X X 0 2X X 2X 2X 2X X 2X 0 0 2X 2X X 2X 0 X X 0 0 2X 2X 0 0
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 0 X 2X X 2X X X X 0 0 X X X X X 2X 2X 2X X 2X X 2X X X X X X 2X X 0 X 0 2X 0 X 2X X X X 0 0 0 2X 2X 2X 0 2X 0 X 0 2X 0 0
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X 0 X 2X X 0 0 0 X 2X X 2X X 0 0 X X 0 X 0 0 X X X 0 2X 2X X 2X 2X X 0 0 2X X 0 X 2X X 2X 0 0 0 X X X X X 2X 0 X 0 2X 2X X
generates a code of length 68 over Z3[X]/(X^2) who´s minimum homogenous weight is 117.
Homogenous weight enumerator: w(x)=1x^0+36x^117+174x^120+42x^121+42x^122+390x^123+168x^124+216x^125+698x^126+312x^127+354x^128+1072x^129+492x^130+588x^131+1570x^132+660x^133+702x^134+1710x^135+888x^136+930x^137+2050x^138+744x^139+840x^140+1438x^141+642x^142+432x^143+964x^144+312x^145+228x^146+410x^147+72x^148+42x^149+170x^150+42x^151+108x^153+58x^156+40x^159+16x^162+16x^165+10x^168+4x^171
The gray image is a linear code over GF(3) with n=204, k=9 and d=117.
This code was found by Heurico 1.16 in 7.32 seconds.