The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X X 1 1 1 X 1 X 1 X 1 1 X 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X X 2X X 2X 0 2X X 2X X 0 X 2X 2X 0 0 2X 0 2X X 2X 0 2X 2X 2X X X 0 2X 0 X X 2X X X 0 2X X X 0 X 0 0 X X 2X 0 X 2X 0 X 0 0
0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X X 2X 0 X 2X 0 2X 0 X X 0 2X 2X X 2X X 2X X X 2X X 0 2X 0 X X 2X 0 2X 0 0 0 2X 2X X 2X 2X X 2X X 2X X X X 2X 0 2X X 2X 0 2X 0
0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 2X 0 0 0 2X 2X 0 X X X X 2X X 2X X X 2X X 0 X 0 0 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 0 X 2X X 0 2X 0 0 2X X 0 X X 0 0 0 0 2X 0
0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X X 2X X 0 X 2X 0 X 0 0 0 2X X 2X X X X 2X X X 2X 0 X X X 2X 2X 0 2X 2X X X 0 X X X 2X 2X 2X 2X X 2X 0 2X X 2X 0 2X 0 X X 0
0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 2X 0 2X X 2X 0 0 X 2X X 2X X 2X 2X 2X 2X 2X 0 X X 2X 0 X 0 0 0 X X 0 0 X 0 0 2X 0 2X 0 0 0 0 0 X X X 0 X X 2X 2X X 0 0
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X 2X 2X 0 X X 0 X 0 0 2X X 0 X 0 2X 0 2X 0 0 0 X X X 0 X 2X 0 2X 0 2X 2X 0 2X X 2X 0 0 0 2X 2X 2X X 2X 2X 0 2X 2X 2X X 2X X
generates a code of length 74 over Z3[X]/(X^2) who´s minimum homogenous weight is 129.
Homogenous weight enumerator: w(x)=1x^0+54x^129+140x^132+214x^135+36x^137+232x^138+162x^140+212x^141+540x^143+198x^144+1170x^146+154x^147+1296x^149+182x^150+918x^152+156x^153+252x^155+152x^156+116x^159+104x^162+88x^165+82x^168+46x^171+20x^174+22x^177+10x^180+2x^186+2x^201
The gray image is a linear code over GF(3) with n=222, k=8 and d=129.
This code was found by Heurico 1.16 in 1.49 seconds.