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 1 X 1 1 1 1 1 0 1 1 X 1 1 1 1 1 1 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 2X+1 2 1 X 0 2X+2 1 1 2X+1 X X+2 X+2 1 1 X 1 X 2X+2 X+2 1 2 2X+1 2X+2 2X+2
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X 2X 0 X 2X 2X 0 2X 2X X 2X X X X 2X 2X 2X X X 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 X 2X 2X 2X 2X X 0 2X 0 X 0 2X X 0 0 2X 2X 2X 0 X 0 X 0 X
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 X 0 X 2X X 0 2X 0 0 X X 0 X X 2X 0 0 X 0 2X 2X X 2X 0
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 2X X X X 0 X X 0 0 X X X 0 X 2X 2X 0 2X 0 0 X 0 X 2X
generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 75.
Homogenous weight enumerator: w(x)=1x^0+136x^75+120x^76+66x^77+328x^78+108x^79+180x^80+492x^81+246x^82+270x^83+678x^84+270x^85+336x^86+858x^87+312x^88+414x^89+678x^90+234x^91+162x^92+286x^93+150x^94+30x^95+102x^96+12x^97+32x^99+6x^100+30x^102+8x^105+10x^108+4x^111+2x^117
The gray image is a linear code over GF(3) with n=129, k=8 and d=75.
This code was found by Heurico 1.16 in 0.747 seconds.