The generator matrix

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

generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+76x^138+246x^141+6x^142+66x^143+474x^144+24x^145+180x^146+946x^147+180x^148+432x^149+1356x^150+516x^151+780x^152+2198x^153+948x^154+1278x^155+3650x^156+1704x^157+1854x^158+4516x^159+2532x^160+2160x^161+5308x^162+2892x^163+2214x^164+4978x^165+2046x^166+1908x^167+4022x^168+1464x^169+1284x^170+2448x^171+672x^172+684x^173+1210x^174+120x^175+180x^176+620x^177+18x^178+84x^179+320x^180+18x^182+176x^183+120x^186+74x^189+32x^192+26x^195+4x^198+2x^201+2x^204

The gray image is a linear code over GF(3) with n=243, k=10 and d=138.
This code was found by Heurico 1.16 in 75.4 seconds.