The generator matrix

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

generates a code of length 52 over Z3[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+26x^90+24x^91+164x^93+408x^94+90x^95+548x^96+1224x^97+684x^98+2896x^99+3066x^100+2844x^101+8152x^102+4290x^103+5418x^104+10716x^105+5016x^106+3690x^107+5460x^108+2844x^109+396x^110+232x^111+540x^112+104x^114+78x^115+52x^117+6x^118+32x^120+24x^123+14x^126+6x^129+2x^132+2x^135

The gray image is a linear code over GF(3) with n=468, k=10 and d=270.
This code was found by Heurico 1.16 in 7.39 seconds.