The generator matrix

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

generates a code of length 75 over Z3[X]/(X^3) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+462x^139+768x^140+2002x^141+3516x^142+4434x^143+5766x^144+9804x^145+9096x^146+10710x^147+16002x^148+15132x^149+14644x^150+19866x^151+15726x^152+13290x^153+13626x^154+8130x^155+5688x^156+4536x^157+1866x^158+910x^159+510x^160+156x^161+140x^162+120x^163+54x^164+54x^165+60x^166+36x^167+12x^168+12x^169+6x^170+12x^172

The gray image is a linear code over GF(3) with n=675, k=11 and d=417.
This code was found by Heurico 1.16 in 79.5 seconds.