The generator matrix

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

generates a code of length 67 over Z3[X]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+456x^116+386x^117+2316x^119+1582x^120+5178x^122+3058x^123+9072x^125+5186x^126+12522x^128+7404x^129+17376x^131+9314x^132+20424x^134+10546x^135+20112x^137+9160x^138+15300x^140+6722x^141+9462x^143+3684x^144+4194x^146+1432x^147+1398x^149+436x^150+222x^152+90x^153+60x^155+20x^156+6x^158+12x^159+6x^162+4x^165+6x^168

The gray image is a linear code over GF(3) with n=201, k=11 and d=116.
This code was found by Heurico 1.16 in 495 seconds.