The generator matrix

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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+366x^147+126x^148+288x^149+1298x^150+1800x^151+1710x^152+2982x^153+3708x^154+3708x^155+4214x^156+5832x^157+5346x^158+5384x^159+6426x^160+4932x^161+3474x^162+3420x^163+1476x^164+1030x^165+522x^166+36x^167+490x^168+36x^169+270x^171+130x^174+26x^177+12x^180+2x^183+2x^186+2x^189

The gray image is a linear code over GF(3) with n=711, k=10 and d=441.
This code was found by Heurico 1.16 in 12.7 seconds.