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 1 1 1 1 1 0 1 X 0 1 1 1 X 1 1 0 X 0 1 X 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 2X+1 0 2 X X X+1 1 2 1 X+2 1 1 2X+2 2 2X+1 0 X+2 2X+1 1 2X 1 1 1 2X+1 1 1 2X+1 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 X X 2X 2X 2X X 0 X X X 2X 0 2X 0 0 X 0 0 X X X 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 0 X 2X 2X 2X 2X 0 2X 2X X X 0 0 X 2X X X 0 X X 2X 0 0 X 2X 2X 2X 0 X 2X 0 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 0 X X 2X 0 2X X 2X X 2X 0 X 0 2X X X X 2X X 2X 0 0 0 2X X X 2X X 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 2X 0 2X X 2X 0 X 2X 0 0 2X 0 X X 0 2X 2X 0 X 2X X 2X X X 0 2X 0 X 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 0 2X X X X 2X 2X 0 0 X 0 0 2X 0 0 0 0 X X 0 X 2X X 0 2X 0 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X X 2X 2X X 0 X 0 0 0 0 X 0 2X X 2X X X 2X 2X 0 2X X 0 2X 0 2X 2X X 2X X 2X 0 0
generates a code of length 53 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+66x^84+188x^87+12x^88+96x^89+370x^90+162x^91+342x^92+386x^93+636x^94+954x^95+556x^96+1554x^97+1896x^98+532x^99+2958x^100+3558x^101+608x^102+4488x^103+5094x^104+660x^105+5712x^106+5334x^107+628x^108+5262x^109+4674x^110+662x^111+3588x^112+2682x^113+610x^114+1470x^115+1260x^116+518x^117+366x^118+336x^119+328x^120+36x^121+18x^122+224x^123+134x^126+52x^129+30x^132+4x^135+4x^138
The gray image is a linear code over GF(3) with n=159, k=10 and d=84.
This code was found by Heurico 1.16 in 41.5 seconds.