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

generates a code of length 52 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+146x^84+296x^87+386x^90+18x^92+498x^93+216x^95+566x^96+1080x^98+564x^99+2880x^101+670x^102+4320x^104+688x^105+3456x^107+668x^108+1152x^110+656x^111+550x^114+328x^117+276x^120+166x^123+78x^126+20x^129+2x^132+2x^138

The gray image is a linear code over GF(3) with n=156, k=9 and d=84.
This code was found by Heurico 1.16 in 8.66 seconds.