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 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 X 1 X 1 1 1 1 1 1 1 2X 1 1 1 1 1 1 1 1 2X 0 0 X 1 1 1 2X 1 1 1 1 1 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 X 2 2X+1 1 2X+1 0 1 2 2X 2X+1 2 1 X+2 1 1 0 2X+2 2X+1 2X X+2 1 2 1 2X+1 2 0 0 2X+1 2X+2 2X+1 1 X+1 X+1 2X X+1 X+2 X+1 2X+1 2X+1 1 1 1 1 1 2X X+1 1 X+2 X X+2 2 2X+1 0 2 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 X 2X X 0 2X 2X 2X 2X 2X X 0 2X 0 2X 0 0 0 2X 0 0 X 0 2X 0 2X 0 0 X 0 2X 0 X X 2X 2X X X 2X 2X 0 X X 0 X 2X 0 2X 2X X 0 X 0 2X 0 2X 0 X 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X X X 0 2X X 0 X X 0 0 0 2X 2X 2X 2X 0 2X X X 2X X X 2X X X 2X 2X X X 0 2X 0 2X X 0 0 0 X 0 0 0 2X 2X 0 0 X 2X 0 2X X 0 2X 2X 2X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 2X X 2X X X X 2X 2X X X 2X X X X X 2X X 0 2X X X X X X 2X 0 2X X X 2X 2X 0 0 2X 2X X 2X 2X 2X X 2X X X 0 0 0 X 2X X 2X 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X X 2X 2X X 0 2X 0 2X 0 2X 0 X 2X 0 2X 0 2X 0 0 X 0 2X X X 2X 2X 0 0 2X 2X 0 2X X X 0 0 X 2X X 0 0 2X 2X 2X 2X 0 2X 2X 2X X X 0 0 0 0 2X 0 2X 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X X X 0 0 X 2X 2X 2X 0 X 0 X 0 2X 2X X 2X X 0 X 2X 0 2X X 0 X 0 0 2X 0 0 0 X 0 X 0 X 2X X X 0 0 2X 0 X 0 X X 0 X X X 0 0 2X X 2X 0 X X
0 0 0 0 0 0 0 X X X X 0 2X X 2X 0 2X 2X 0 0 2X X 2X 2X 0 2X X 0 2X X 2X X 0 X 0 0 X X 2X 2X 0 0 0 X X 0 X X X 0 X 2X 0 X 0 X X 2X X 0 X X 2X X 0 0 0 0 0 2X 0 0 X 2X 2X
generates a code of length 75 over Z3[X]/(X^2) who´s minimum homogenous weight is 126.
Homogenous weight enumerator: w(x)=1x^0+60x^126+6x^128+214x^129+18x^130+18x^131+328x^132+198x^133+174x^134+412x^135+624x^136+558x^137+468x^138+1122x^139+1290x^140+510x^141+2130x^142+2502x^143+512x^144+3420x^145+3972x^146+508x^147+4464x^148+5028x^149+574x^150+4770x^151+5364x^152+558x^153+4410x^154+3894x^155+536x^156+2808x^157+2346x^158+508x^159+1476x^160+870x^161+372x^162+618x^163+156x^164+378x^165+174x^166+66x^167+248x^168+12x^169+186x^171+100x^174+40x^177+32x^180+8x^183+6x^186+2x^192
The gray image is a linear code over GF(3) with n=225, k=10 and d=126.
This code was found by Heurico 1.16 in 67.8 seconds.