The generator matrix

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

generates a code of length 52 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+700x^90+2748x^93+5388x^96+7826x^99+10146x^102+11262x^105+10232x^108+6822x^111+2952x^114+806x^117+156x^120+10x^126

The gray image is a linear code over GF(3) with n=156, k=10 and d=90.
This code was found by Heurico 1.16 in 47.1 seconds.