The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 2X 1 1 1 0 0 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 2 2X+1 1 0 2 0 1 2X+1 2X+1 X+1 2 X 2X+1 2X X 2X 1 1 2 2X X+2 1 1 2X+1 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 X 2X X 0 2X 0 2X 2X 2X 2X 0 0 X 2X 0 X X X X 2X 0 X 0 0 0 X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X 0 2X 2X X 2X 0 X 2X 0 X X 0 X X X 2X X 0 X X X 0 X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X X 0 X X 2X X 0 2X 0 0 X 2X 2X X 0 X X 2X X X 2X 0 0 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X X 0 0 2X 2X 0 2X X 2X 0 2X 2X 2X 0 0 2X 0 2X X 2X 2X X 2X X 0 0 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 2X 0 0 2X 0 2X 2X X 0 X 0 2X 0 2X X X X 0 2X 0 X X 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X 0 2X 0 X 0 0 0 0 2X 2X 2X 0 2X X 2X 0 0 2X 0 0 2X 2X 0 X 2X 0 0
generates a code of length 45 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.
Homogenous weight enumerator: w(x)=1x^0+60x^69+192x^72+30x^73+30x^74+400x^75+204x^76+234x^77+410x^78+702x^79+720x^80+526x^81+1680x^82+2196x^83+580x^84+3432x^85+4446x^86+652x^87+5634x^88+6228x^89+730x^90+6234x^91+6264x^92+808x^93+4854x^94+4068x^95+644x^96+2574x^97+1800x^98+600x^99+804x^100+258x^101+428x^102+96x^103+310x^105+130x^108+50x^111+26x^114+8x^117+2x^120+4x^123
The gray image is a linear code over GF(3) with n=135, k=10 and d=69.
This code was found by Heurico 1.16 in 32.5 seconds.