The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 1 1 0 1 2X 1 2X 1 1 0 1 1 1 1 0 1 1 0 1 1 1 X 1 1 1 1 1 1 1 1 0 0 1 2X 1 1 1 1 1 X 1 1 1 0 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 0 2X+1 2 X+1 0 2 X 1 2X+1 1 2 1 2X 2X+2 1 2X+1 0 2X+1 2X+2 1 2 X 1 X+1 X+1 1 1 2X 2X 1 2 2X+2 0 X+2 2X+1 1 1 2X 1 X 0 X+2 2X 1 1 X+2 X+1 X X 2X 0 2 2X+1
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X 0 X 2X 2X X X X X X 2X X 0 2X 2X 2X 2X 0 X X X 0 X 2X 0 0 X 0 X X X 0 2X X 0 0 0 X 0 X X X X 2X 2X 0 X 0 2X 0 X 2X
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X X 2X 0 2X 0 2X 2X X 0 X 0 X X 0 2X X 2X 2X X X X 0 0 X 2X X 2X 2X 2X X 0 0 X 2X 0 X 2X 0 X 0 0 X X X 0 2X 2X X 2X X 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X 0 2X 2X X 2X 0 2X X X X 2X 0 0 X 2X 0 X 2X X 0 X 0 2X X X X 2X 0 0 X 0 2X 2X 2X 0 X 0 2X 0 0 0 2X 2X 2X 0 X 0 2X 0 2X 0 2X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 0 X X X X X X 0 X 0 2X 2X 0 0 X 2X X 0 2X 0 X 2X 2X X 0 X X 0 2X 0 2X X 2X 2X 2X 0 2X 0 0 0 0 X 0 X 2X X 2X 0 0 2X X X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X X 2X X 0 X X 2X X 0 X X 2X X X 0 2X 2X 0 X X 0 2X 0 X X X 0 0 0 0 0 2X X 0 0 2X X 0 X 2X 0 X X X X X X 2X 2X 0 0 X
generates a code of length 70 over Z3[X]/(X^2) who´s minimum homogenous weight is 123.
Homogenous weight enumerator: w(x)=1x^0+128x^123+30x^124+120x^125+178x^126+186x^127+312x^128+222x^129+546x^130+660x^131+230x^132+804x^133+1134x^134+206x^135+1350x^136+1260x^137+182x^138+1572x^139+1488x^140+176x^141+1668x^142+1548x^143+180x^144+1458x^145+1242x^146+174x^147+798x^148+696x^149+128x^150+252x^151+222x^152+104x^153+84x^154+48x^155+90x^156+18x^158+80x^159+44x^162+28x^165+14x^168+14x^171+6x^174+2x^180
The gray image is a linear code over GF(3) with n=210, k=9 and d=123.
This code was found by Heurico 1.16 in 14 seconds.