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.