The generator matrix
1 0 0 1 1 1 1 1 0 1 1 1 2X 1 1 0 1 X 1 1 1 1 1 0 1 X 1 0 0 1 1 1 1 2X 1 1 1 1 1 1 1 2X 1
0 1 0 1 0 2 1 2 1 0 2X+1 2X+2 1 X+1 2 1 2X 1 2X+2 2X+1 X 1 0 1 2 1 X+1 1 1 X+1 2X+1 X+1 X 0 0 X+2 X X+1 2X+1 1 X+2 1 0
0 0 1 2 1 2 1 0 2 2 2X 2X+1 2X+1 2X+2 2 2X X+1 1 2X+1 2X X+2 1 2X X+2 2X 2X 2X+2 2 X+1 2X+1 2X+2 X 2X+1 1 2X 2X 2X+1 2X+1 2X 2X+1 1 2X+2 0
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X X 2X 2X X X 2X X 2X X X 0 X 2X 0 2X 0 0 X 2X X 2X X 0 0 X X X 0 0
0 0 0 0 2X 0 0 0 X X 2X 2X X 2X X X 0 X 2X 0 2X X X 0 X X 0 0 0 2X 0 X 2X X X 2X X 0 0 2X 2X 0 0
0 0 0 0 0 X 0 X X 0 X 0 2X X 2X 0 2X X X 2X 2X 2X 0 0 X 2X X 0 X 0 X X 2X 2X 0 0 0 2X 2X 0 X 0 0
0 0 0 0 0 0 X 2X X X 0 2X 2X 2X 0 2X 2X 0 0 X 0 0 X X X X 0 X X 2X 2X 2X 0 X 0 2X 0 2X X 2X 2X 2X 2X
generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.
Homogenous weight enumerator: w(x)=1x^0+38x^69+6x^70+114x^71+150x^72+390x^73+552x^74+282x^75+1260x^76+1644x^77+502x^78+2232x^79+2766x^80+796x^81+4110x^82+4434x^83+1150x^84+5634x^85+6162x^86+1484x^87+5796x^88+5484x^89+1126x^90+4254x^91+3444x^92+522x^93+1908x^94+1320x^95+258x^96+606x^97+276x^98+100x^99+48x^100+48x^101+90x^102+40x^105+14x^108+8x^111
The gray image is a linear code over GF(3) with n=129, k=10 and d=69.
This code was found by Heurico 1.16 in 27.5 seconds.