The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+68x^93+48x^95+196x^96+294x^98+368x^99+882x^101+568x^102+1368x^104+784x^105+2304x^107+1012x^108+2898x^110+1266x^111+2646x^113+1018x^114+1764x^116+634x^117+756x^119+294x^120+150x^122+134x^123+12x^125+98x^126+70x^129+26x^132+20x^135+2x^138+2x^141

The gray image is a linear code over GF(3) with n=165, k=9 and d=93.
This code was found by Heurico 1.16 in 5.6 seconds.