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

generates a code of length 53 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+68x^84+222x^87+296x^90+464x^93+90x^95+482x^96+540x^98+562x^99+1620x^101+552x^102+3330x^104+670x^105+4158x^107+760x^108+2592x^110+624x^111+792x^113+600x^114+448x^117+340x^120+268x^123+110x^126+54x^129+26x^132+10x^135+4x^138

The gray image is a linear code over GF(3) with n=159, k=9 and d=84.
This code was found by Heurico 1.16 in 8.7 seconds.