The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1  1  X  X  X  1  1  1  1  1  1  1  1  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X 2X 2X  X 2X 2X 2X  0  X  X  X 2X  X  X 2X  X  0  X  X  X  0 2X 2X  0  X  0  X 2X 2X  0  0  X  0  X  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  X 2X 2X 2X 2X  0  X  X 2X  X 2X  0  X  X  0  X  0  X  0  X 2X  0  0  X  0  X  X  X  0  X  X  X  X 2X  0 2X  0 2X  X 2X
 0  0  0  X  0  0  0  0  X 2X 2X 2X  0  0  X  0  X 2X 2X  0  X  0 2X  X  0  0  X 2X  X  0 2X  X 2X  0  X 2X  0  0  X  X  0  X 2X 2X  X 2X 2X  X  0  0  X
 0  0  0  0  X  0  0  X 2X  0 2X  0  0 2X 2X  X  X  X  0 2X 2X 2X  X 2X  X  X  X  0  0 2X 2X  X  0  0  0  0  0 2X  0 2X 2X  X  0  0  X  X  X  0 2X  X  0
 0  0  0  0  0  X  0 2X 2X  X  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  X  0  X  0 2X  X  0  0 2X  X  X  X  0 2X 2X  0 2X  X  X 2X  0  X 2X 2X  X 2X 2X  X  0  0
 0  0  0  0  0  0  X 2X 2X 2X 2X 2X 2X  X  X  X  0 2X  X 2X 2X 2X  X  0 2X 2X  X  X  X 2X  X 2X  X  X  0  X  0 2X  0  0  X 2X  0  X  0  X 2X 2X  X  X  0

generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+202x^87+200x^90+30x^91+126x^93+180x^94+318x^96+540x^97+198x^99+1110x^100+146x^102+1386x^103+244x^105+864x^106+222x^108+264x^109+144x^111+182x^114+94x^117+66x^120+24x^123+12x^126+4x^129+2x^132+2x^135

The gray image is a linear code over GF(3) with n=153, k=8 and d=87.
This code was found by Heurico 1.16 in 1.51 seconds.