The generator matrix

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

generates a code of length 53 over Z3[X]/(X^2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+180x^89+334x^90+558x^91+1320x^92+1556x^93+1752x^94+2748x^95+2988x^96+3360x^97+5244x^98+6016x^99+6072x^100+8442x^101+8396x^102+8514x^103+11532x^104+11274x^105+10374x^106+13116x^107+11432x^108+9840x^109+11220x^110+9170x^111+7008x^112+7272x^113+5102x^114+3684x^115+3240x^116+2168x^117+1026x^118+1050x^119+494x^120+276x^121+210x^122+88x^123+24x^124+36x^125+14x^126+2x^129+4x^132+6x^135+2x^138+2x^141

The gray image is a linear code over GF(3) with n=159, k=11 and d=89.
This code was found by Heurico 1.16 in 384 seconds.