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 0 1 1 1 1 2X 1 1 0 1 1 1 0 2X 1 X 1 1 X 1 1 1 1 2X 1 1 0 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 1 1 2X+1 2 0 2 0 1 0 2X+1 X+1 2X+1 1 2 X+2 1 X 2X+1 X+2 1 1 X 1 2X+2 2X 1 X+1 2X 2X+1 2X+2 1 2X X 1 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 2X 2X X 2X X 2X X 2X X 0 X 0 2X 2X 2X 0 2X X 2X 2X 0 0 2X X X X 0 0 0 2X 2X 0 2X 2X 2X X 0 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X X X 2X 0 X X 2X 0 X 0 X 2X 2X 2X X 2X 2X 0 0 2X 2X X 0 2X X 0 X X 0 2X 0
0 0 0 0 X 0 0 0 X 2X 2X X 2X X 2X 0 2X 0 X X X X X X 0 0 X X X 2X 2X 2X 0 X X X 0 2X 0 0 2X 2X X X 0 X 2X X X 2X 0
0 0 0 0 0 2X 0 X 2X 2X 2X 0 X 0 2X X X 0 X 2X 0 2X X 0 X 0 0 0 2X 2X X 2X X 0 X 2X 2X 2X X 0 0 2X X 2X 0 2X X X 0 2X 0
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X X X 0 2X 2X 2X 0 2X 2X 0 X 0 2X X 0 0 0 X 0 X X 2X 0 X 2X X 2X 2X 0 X X 2X 0 X 2X X 2X 0
generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+52x^84+6x^86+166x^87+96x^89+300x^90+588x^92+556x^93+1122x^95+750x^96+2016x^98+912x^99+2964x^101+1056x^102+3174x^104+1034x^105+2088x^107+778x^108+822x^110+460x^111+234x^113+220x^114+12x^116+128x^117+88x^120+44x^123+14x^126+2x^129
The gray image is a linear code over GF(3) with n=153, k=9 and d=84.
This code was found by Heurico 1.16 in 4.91 seconds.