The generator matrix

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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+1296x^160+2352x^161+4770x^162+8088x^163+11010x^164+14562x^165+20430x^166+23820x^167+27946x^168+35244x^169+38718x^170+42394x^171+49902x^172+46986x^173+44574x^174+43464x^175+35604x^176+27198x^177+21906x^178+13344x^179+8312x^180+5160x^181+2340x^182+942x^183+528x^184+210x^185+104x^186+66x^187+66x^188+14x^189+30x^190+18x^191+18x^193+6x^195+6x^196+6x^197+6x^198

The gray image is a linear code over GF(3) with n=774, k=12 and d=480.
This code was found by Heurico 1.16 in 718 seconds.