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

generates a code of length 53 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+114x^90+206x^93+216x^96+222x^99+162x^100+192x^102+972x^103+210x^105+1944x^106+200x^108+1296x^109+212x^111+196x^114+144x^117+126x^120+68x^123+48x^126+20x^129+10x^132+2x^150

The gray image is a linear code over GF(3) with n=159, k=8 and d=90.
This code was found by Heurico 1.16 in 1.03 seconds.