The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 X 1 1 X 1 2X 1 1 1 2X 2X 1 1 1 1 1 1 1 0 1 2X X 2X 1 0 X 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 2X+1 1 2 0 2 X 1 2X+1 X+1 0 2 1 0 2X+1 X+2 2X+1 2 0 2X+1 1 X+2 2X X+2 1 2X 1 2X+1 2X 1 1 2 1 0 1 1 X 0 1 1 2 1 X+1 X+1 2X X+2 X+2 1 2 1 0 1 2X+1 1 1 2X+1 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 X 2X X 0 X 2X 2X 0 2X 0 2X X 2X 2X 0 0 X X X 0 0 X 2X X X 2X 2X 2X 2X X 0 X X 2X X X 0 X X X 0 X X X 2X X 0 2X 2X 2X 0 0 0 2X X 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X X X X 2X 0 0 X X 2X 0 2X 2X 2X 0 2X 0 0 X 0 2X 2X 0 X 0 X 2X X X 0 X 0 X 2X 2X 0 2X 2X X 2X X 2X 2X X 2X 0 0 0 2X 2X 0 0 2X X X
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 2X 2X X 2X X 2X 2X X X X 2X X 2X X 2X 2X X X 0 X X X X X X 2X 2X 0 0 0 X X 2X X X 0 2X X X 2X 0 0 0 2X 2X 2X 2X 0 0 2X 2X X
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X X 2X 2X X 0 0 2X 2X X 0 X X X X X 2X 0 2X 2X 0 0 0 0 X 0 X 2X 2X X 0 2X 0 0 X 2X 0 X 2X X 2X 0 2X 2X 0 2X 2X 2X 0 0 X X 0 X 0 X 0 2X
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X X X 0 0 X X 2X 0 0 0 2X X X 2X 2X 2X 0 0 0 0 0 2X X 0 X 2X X 2X 2X 0 2X X 2X 2X 0 2X X 0 0 0 2X X X 0 2X 0 2X X 2X 0 X X X 0 X 2X 0 X
0 0 0 0 0 0 0 X X X X 0 2X X 2X 0 2X 2X 0 0 X 2X 0 X X 2X 0 0 X 0 2X 2X 2X 2X 2X X 0 2X 0 2X 0 2X 0 2X X 0 X 0 0 0 X 2X 0 0 2X X 0 X X X X 0 X 2X 2X X 0 X X 0 2X 0 X
generates a code of length 73 over Z3[X]/(X^2) who´s minimum homogenous weight is 123.
Homogenous weight enumerator: w(x)=1x^0+88x^123+284x^126+54x^127+404x^129+384x^130+690x^132+1008x^133+1044x^135+2046x^136+1566x^138+3900x^139+2324x^141+5712x^142+2822x^144+7356x^145+2994x^147+7272x^148+2754x^150+5820x^151+2010x^153+3738x^154+1116x^156+1560x^157+682x^159+420x^160+378x^162+90x^163+250x^165+6x^166+140x^168+74x^171+40x^174+18x^177+2x^180+2x^183
The gray image is a linear code over GF(3) with n=219, k=10 and d=123.
This code was found by Heurico 1.16 in 65.9 seconds.