The generator matrix

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

generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+64x^90+126x^91+48x^92+302x^93+426x^94+258x^95+688x^96+1224x^97+690x^98+1418x^99+2184x^100+1266x^101+2088x^102+3414x^103+1902x^104+3174x^105+4326x^106+2622x^107+3726x^108+5196x^109+2760x^110+3546x^111+4512x^112+1920x^113+2638x^114+3030x^115+1164x^116+1268x^117+1182x^118+408x^119+456x^120+504x^121+78x^122+168x^123+114x^124+6x^125+76x^126+6x^127+32x^129+28x^132+8x^135+2x^138

The gray image is a linear code over GF(3) with n=162, k=10 and d=90.
This code was found by Heurico 1.16 in 38 seconds.