The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 0 1 1 1 1 0 1 1 1 1 2X 1 1 1 1 1 1 0 2X 1 1 X 2X 1 1 0 1 1 1 0 1 2X X 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 X 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 1 0 2X+2 2X+1 X 1 2X+1 2 X 2 1 X+1 2 X 1 2X+1 X+2 1 1 2X+1 X+2 1 1 0 X+2 1 0 X 2X+1 1 2 1 1 2X+1 2X+1 2X+2 X+2 2X 2X+2 X+2 1 2 2X 2X+2 X+2 2 2 X+1 0 2X+1 X+1 1 0 1 0 2 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X X 0 X 2X X 2X 2X X 0 X 0 2X 2X 2X 0 2X X X 0 2X 2X X 0 X 2X 2X 0 0 X X X 2X 2X 2X X X 0 2X X 2X 0 2X 2X X 0 0 2X 0 0 X X X 0 X 0 X 0 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X 2X 2X X X X X 0 2X X X X 0 X 2X 2X 0 2X X 2X 0 2X X X X 0 X X 2X 0 X 2X 0 X X 0 2X 0 2X X 2X X X X 0 0 2X X 2X X X 2X X 2X X 0 X 2X 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X 0 X X 2X X 0 0 0 X 2X X 2X 0 0 X 2X 2X 0 2X 0 2X 0 2X 2X X X 0 2X 0 2X 0 X X 2X X 2X 2X 2X X X 0 2X X X X 0 0 2X 0 2X X X X X 0 0 2X 0 0
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 2X 0 0 2X 2X 0 2X 0 0 X 0 2X X X 0 0 0 X 2X 2X 2X 2X 2X 2X 2X 2X 0 X X 2X X 2X 2X 0 X 0 2X 2X 2X X 2X X 2X 0 2X 2X X X 0 X 0 X 2X 0 0 2X 0 X 2X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X 2X 2X X 2X 2X 0 X X 0 2X 0 0 0 2X 2X X 0 2X 0 X 2X 2X X X X 2X 2X 0 X 2X 0 X 0 2X X 2X 2X X 2X X X X 2X 2X 0 2X 0 X X 2X X 0 X 0 0 0 X 2X 0
generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 135.
Homogenous weight enumerator: w(x)=1x^0+32x^135+12x^136+214x^138+114x^139+386x^141+486x^142+586x^144+900x^145+680x^147+1602x^148+668x^150+1974x^151+802x^153+2508x^154+984x^156+2358x^157+778x^159+1848x^160+624x^162+948x^163+320x^165+300x^166+202x^168+66x^169+106x^171+6x^172+54x^174+60x^177+34x^180+14x^183+10x^186+2x^189+2x^192+2x^195
The gray image is a linear code over GF(3) with n=231, k=9 and d=135.
This code was found by Heurico 1.16 in 8.68 seconds.