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.