The generator matrix

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

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+378x^147+1296x^148+1746x^149+3850x^150+4938x^151+5976x^152+8816x^153+10356x^154+11250x^155+14124x^156+15174x^157+15984x^158+16660x^159+15954x^160+13752x^161+13150x^162+9120x^163+5490x^164+4092x^165+2304x^166+1116x^167+754x^168+366x^169+90x^170+92x^171+174x^172+36x^174+72x^175+12x^177+18x^178+6x^181

The gray image is a linear code over GF(3) with n=711, k=11 and d=441.
This code was found by Heurico 1.16 in 84.8 seconds.