The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 2X 2X^2+X  1  1  1  1  1  1  1  0 2X 2X  1  1  1 X^2+2X  1  1  1 2X  1 X^2+X  1  1  1  1  1 2X^2+2X  1  1  1  1 X^2+2X  1  1 2X^2+X X^2  1  1  1
 0  1  0  0 X^2 2X^2+2X+1 2X^2+2X+1  1 2X^2+2X+2  2 X+2  1  1 X^2+X 2X^2+X+2 2X^2+X 2X^2+1 X^2+X+1  2 X^2+X+2  1  1 2X 2X^2+2X+1 X+1 2X^2+2X  1 X+2 2X^2+X+1 X^2+2X  1 X^2  1  1 2X+2 2X+2  1 2X^2+X  1 2X^2+1  2 X+2  X  1 2X^2+X+1  1  1  1 2X 2X^2+2X+1 X^2+X
 0  0  1  1 2X^2+2 2X^2+2 2X^2+2X  1 2X^2+2X+2  X 2X+1 X+1 2X^2+2X+2 X^2+2X+2 X^2 X+1 2X 2X^2+X+2  2 X^2+2X+1  0 X^2+2X+2  1 2X+2 2X+1 2X X+1 2X^2+2X+2 2X^2+X X^2+1 X+2 X^2+2  1 2X+1 X^2  1 X^2+2X+1  X X^2 X^2+2X 2X^2+2X+1 X^2+1  2 2X^2+2X X^2+2 X^2+X+2 X+1 X^2+2 X+1 2X^2 X^2+X
 0  0  0 2X 2X^2 X^2  0 X^2+2X 2X^2+X  X 2X^2  0 2X^2 X^2+X 2X^2+2X X^2  X  X 2X^2+2X 2X 2X 2X X^2+2X X^2+2X X^2+X 2X^2+2X X^2+2X X^2 2X X^2+X 2X^2+X 2X^2+2X  X  0  0  X X^2+X 2X^2+X X^2+X 2X^2+X X^2+2X 2X^2+X 2X^2 2X^2+X X^2+2X X^2 X^2  0 X^2+X 2X^2+2X 2X

generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+390x^92+562x^93+1998x^94+3456x^95+4470x^96+7020x^97+9222x^98+12240x^99+16368x^100+18132x^101+20808x^102+21666x^103+20250x^104+15472x^105+11544x^106+6876x^107+3320x^108+1938x^109+822x^110+164x^111+150x^112+126x^113+50x^114+48x^115+12x^116+12x^117+18x^118+6x^119+6x^120

The gray image is a linear code over GF(3) with n=459, k=11 and d=276.
This code was found by Heurico 1.16 in 48.9 seconds.