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

generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+190x^84+454x^87+648x^90+876x^93+18x^94+1144x^96+252x^97+1436x^99+1512x^100+1800x^102+5040x^103+2018x^105+10080x^106+2036x^108+12096x^109+2190x^111+8064x^112+2094x^114+2304x^115+1714x^117+1288x^120+794x^123+502x^126+276x^129+130x^132+60x^135+20x^138+8x^141+2x^144+2x^147

The gray image is a linear code over GF(3) with n=162, k=10 and d=84.
This code was found by Heurico 1.16 in 89.1 seconds.