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

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+680x^90+2748x^93+5436x^96+7948x^99+9858x^102+11292x^105+10538x^108+6504x^111+3078x^114+832x^117+114x^120+12x^123+8x^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 53.3 seconds.