The generator matrix

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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+294x^123+504x^124+1614x^125+3182x^126+3390x^127+6306x^128+8772x^129+8244x^130+13218x^131+15808x^132+13356x^133+20040x^134+19488x^135+14310x^136+16200x^137+13088x^138+6930x^139+5964x^140+3600x^141+1212x^142+726x^143+450x^144+96x^145+66x^146+136x^147+54x^148+6x^149+62x^150+12x^151+12x^152+6x^154

The gray image is a linear code over GF(3) with n=603, k=11 and d=369.
This code was found by Heurico 1.16 in 69.5 seconds.