The generator matrix

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

generates a code of length 63 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+166x^108+366x^109+624x^110+1134x^111+1536x^112+1788x^113+2362x^114+3162x^115+3162x^116+4242x^117+5520x^118+5124x^119+6666x^120+8520x^121+7290x^122+8974x^123+10872x^124+9000x^125+10372x^126+11664x^127+9168x^128+9910x^129+10794x^130+7914x^131+7976x^132+7440x^133+5070x^134+4556x^135+3942x^136+2382x^137+2014x^138+1398x^139+774x^140+532x^141+342x^142+156x^143+106x^144+54x^145+36x^146+16x^147+10x^150+6x^153+6x^156

The gray image is a linear code over GF(3) with n=189, k=11 and d=108.
This code was found by Heurico 1.16 in 489 seconds.