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 1 1 1 0 1 1 1 0 1 1 1 X 2X 1 1 0 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 1 2 2X+1 0 2 2 0 2X+1 1 X 2X+1 2 1 2X X+1 2X 1 1 0 1 1 2X+1 1 1 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X X 0 2X 2X 2X X 0 2X 2X X 2X 0 X X 0 X 2X X X X 2X 0 0 X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X 0 X 2X 2X 0 2X 2X X X 2X X X 0 X 2X 0 0 2X 2X X 0 2X 2X 2X 2X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 2X 0 2X X 0 2X 2X X 2X 2X X X 0 0 2X X 0 2X 2X X X X X 2X 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 X 0 X 2X 0 2X 0 0 0 X 2X 0 X 0 X 2X X 2X X 0 2X X X X 0 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X 0 X 0 X X X 2X 0 X X 2X 0 0 X X X 2X 2X 2X 0 2X X 0 0 X
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X X 2X 2X X X 0 2X 0 X 2X X 2X 0 0 2X 2X 2X 0 2X X 2X 0 X 0 2X 2X
generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+100x^72+264x^75+6x^76+6x^77+604x^78+102x^79+108x^80+1228x^81+426x^82+480x^83+2326x^84+1092x^85+1266x^86+4034x^87+2172x^88+2682x^89+6438x^90+3090x^91+3720x^92+6490x^93+3144x^94+2940x^95+5770x^96+2100x^97+1584x^98+3242x^99+858x^100+336x^101+1344x^102+132x^103+566x^105+232x^108+104x^111+40x^114+18x^117+2x^120+2x^123
The gray image is a linear code over GF(3) with n=138, k=10 and d=72.
This code was found by Heurico 1.16 in 34.6 seconds.