The generator matrix

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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+44x^96+156x^97+264x^98+700x^99+816x^100+882x^101+1508x^102+1356x^103+1506x^104+2322x^105+1908x^106+2430x^107+3482x^108+2652x^109+2778x^110+4462x^111+3096x^112+3240x^113+4328x^114+3240x^115+3060x^116+3854x^117+2286x^118+2166x^119+2160x^120+1362x^121+918x^122+920x^123+468x^124+240x^125+210x^126+132x^127+6x^128+28x^129+18x^130+6x^131+16x^132+6x^133+4x^135+14x^138+2x^141+2x^144

The gray image is a linear code over GF(3) with n=168, k=10 and d=96.
This code was found by Heurico 1.16 in 40.9 seconds.