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 1 1 0 0 1 1 1 1 0 1 1 2X 1 1 1 1 2X 1 1 1 1 2X 1 X 1 0 1 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 0 2X+1 0 2 1 1 2X+2 2X+1 X 2 1 2X+1 2 1 X 2 X+1 X 1 X X X+1 X+1 1 1 2X X+2 1 X 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X X 0 X 2X X 2X X 2X 0 0 2X 0 0 2X 0 X 0 2X 0 X 2X 2X 0 2X 2X 0 0 X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X X 2X X 0 X X 0 X X X X X 2X X 0 2X X 2X 0 0 0 2X 0 X 0 2X 2X 0 X X X
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 0 X X 2X X 2X 0 0 X 0 X X 2X 2X X X X 2X 2X 2X 0 X X 2X 2X 0 2X 2X X X
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 0 X 2X X X 2X 0 2X 0 2X 2X X 0 X 2X 0 0 0 2X 2X 2X 0 0 2X X X 0 X 0 X 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 0 2X X 2X X X 0 X X X X 0 2X 2X 2X X 0 X 0 2X 2X X 2X 2X 2X 2X X 2X X
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X 2X 2X 2X X 2X 0 2X X 2X 2X 0 X 2X X 0 0 2X X 2X 2X 0 2X 2X 2X 0 2X 0 X 2X 2X X
generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.
Homogenous weight enumerator: w(x)=1x^0+78x^81+232x^84+66x^85+376x^87+384x^88+716x^90+1182x^91+1182x^93+2892x^94+2028x^96+4986x^97+3020x^99+8322x^100+3874x^102+8670x^103+3612x^105+6876x^106+2290x^108+4236x^109+1074x^111+1494x^112+582x^114+228x^115+320x^117+30x^118+160x^120+94x^123+26x^126+12x^129+4x^132+2x^135
The gray image is a linear code over GF(3) with n=153, k=10 and d=81.
This code was found by Heurico 1.16 in 39.6 seconds.