The generator matrix

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

generates a code of length 84 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+82x^144+278x^147+18x^148+6x^149+502x^150+114x^151+138x^152+830x^153+312x^154+426x^155+1478x^156+624x^157+690x^158+2342x^159+1176x^160+1236x^161+3332x^162+1662x^163+1944x^164+4558x^165+2094x^166+2436x^167+5268x^168+2274x^169+2262x^170+5254x^171+2058x^172+1980x^173+3764x^174+1536x^175+1206x^176+2474x^177+810x^178+576x^179+1216x^180+342x^181+186x^182+642x^183+102x^184+36x^185+340x^186+180x^189+116x^192+78x^195+34x^198+14x^201+12x^204+6x^207+4x^210

The gray image is a linear code over GF(3) with n=252, k=10 and d=144.
This code was found by Heurico 1.16 in 79.3 seconds.