The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 1 0 1 1 0 1 1 1 1 X 1 1 1 1 X 1 1 2X 1 2X 1 1 1 1 1 2X X 1 1 1 1 1 1 1 X 1 1 1 1 0 X 1 1 1 1 2X 1 1 1 1 1 1 1 1 0
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 2X+1 0 1 2 2X+1 1 2 X 2 2X+1 1 2 0 X X+1 1 X+1 2X+2 1 X+1 1 2X+2 1 1 X X+1 1 1 2X X+1 1 2X+2 X+2 X+1 2X+2 1 X+1 2X 2X+1 X+1 1 1 2X 2X 2X+2 X+2 1 X+1 X+1 2 0 X+1 2X+2 2X X+1 1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 2X X 0 2X 2X 2X X X X X 2X X 2X 0 0 0 2X 0 X 2X 2X X 0 2X 0 2X 2X 2X 0 2X X X 0 0 0 X 0 0 X 0 2X 0 X 2X 0 X 0 X 2X 0 2X 2X 0 X 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 0 2X 2X 2X X X 2X 2X 2X X 2X X 0 X 2X 2X X 0 0 X 0 0 2X X 0 X X 0 2X X 0 X X 0 X 2X 0 X X 0 0 0 2X X 2X 0 X 2X X 2X 2X X 0 X 2X 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 X 0 0 X 2X 2X 0 0 X X 2X X 2X X 2X X X X 0 0 2X 2X X 2X 0 0 2X 2X 2X X 2X 2X 2X 2X 0 2X X 0 2X 0 X 0 X X 0 X 2X 0 0 X X 2X 2X 2X 0
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 0 0 X 0 2X 2X X 0 0 0 2X 2X X X 0 2X 2X 0 0 X X X 0 2X 2X 2X X 0 X 0 0 X X 2X X 2X 0 0 0 2X X 2X 2X X 0 0 2X X X 0 X 0 X 2X X
generates a code of length 75 over Z3[X]/(X^2) who´s minimum homogenous weight is 137.
Homogenous weight enumerator: w(x)=1x^0+42x^137+184x^138+66x^139+138x^140+412x^141+144x^142+156x^143+468x^144+204x^145+228x^146+510x^147+264x^148+234x^149+538x^150+270x^151+180x^152+580x^153+258x^154+180x^155+490x^156+156x^157+168x^158+288x^159+72x^160+96x^161+70x^162+24x^163+36x^164+22x^165+20x^168+20x^171+14x^174+14x^177+4x^180+4x^183+6x^186
The gray image is a linear code over GF(3) with n=225, k=8 and d=137.
This code was found by Heurico 1.16 in 1 seconds.