The generator matrix

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

generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+176x^93+174x^94+384x^95+1004x^96+828x^97+1176x^98+1900x^99+1500x^100+1788x^101+2800x^102+2460x^103+2616x^104+3532x^105+2976x^106+3024x^107+4384x^108+3426x^109+3288x^110+4462x^111+3036x^112+2802x^113+3188x^114+1932x^115+1626x^116+1778x^117+852x^118+648x^119+640x^120+270x^121+138x^122+138x^123+42x^124+6x^125+46x^126+2x^129+4x^132+2x^138

The gray image is a linear code over GF(3) with n=162, k=10 and d=93.
This code was found by Heurico 1.16 in 46.5 seconds.