The generator matrix

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

generates a code of length 82 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+64x^144+24x^145+96x^146+462x^147+306x^148+240x^149+1220x^150+468x^151+588x^152+2076x^153+876x^154+1044x^155+2920x^156+1308x^157+1488x^158+3930x^159+1596x^160+1866x^161+4544x^162+1986x^163+2184x^164+5072x^165+2316x^166+2100x^167+4710x^168+1920x^169+1686x^170+3566x^171+1206x^172+954x^173+2310x^174+696x^175+654x^176+1178x^177+336x^178+180x^179+468x^180+66x^181+42x^182+120x^183+18x^184+68x^186+42x^189+20x^192+14x^195+12x^198+4x^201+4x^204

The gray image is a linear code over GF(3) with n=246, k=10 and d=144.
This code was found by Heurico 1.16 in 65.7 seconds.