The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+462x^124+792x^125+2916x^126+5736x^127+8568x^128+12734x^129+16620x^130+22926x^131+28784x^132+34224x^133+44556x^134+50362x^135+53256x^136+52998x^137+51628x^138+45774x^139+37158x^140+26224x^141+16242x^142+9900x^143+5416x^144+2424x^145+912x^146+456x^147+138x^148+36x^149+72x^150+66x^151+30x^152+12x^153+18x^154

The gray image is a linear code over GF(3) with n=612, k=12 and d=372.
This code was found by Heurico 1.16 in 548 seconds.