The generator matrix

 1  0  0  0  0  1  1  1 2X  0 2X 2X  1  1 2X  X  1  1  1 2X 2X  1  1  1  1  1  1  1 2X  1 2X  1  1  1  1  0  0  1  1  1  1  0  1  1 2X 2X  1  1  1  1  1  1  1  0  1  1  1  1  1  0  1  X  0  X  1  1  1  1  1  1  X  1  1  1  X  1  0  1  1  1 2X  1
 0  1  0  0  0  0  0  0  0  1  1  1 X+2 2X+2 2X  X  2 2X+2 2X  1  X X+2  2 2X+1  0  X 2X  1  1  2  0 X+2 X+1 2X+1  X  1  0  1 2X+2  X  2  1 2X+1  X  1  1  1  2  X X+1 X+1 2X+2  2  1  0  X X+2 X+2 X+1  1  2  1  1  1  X 2X+2 2X+2  2 X+2 X+2  1 2X+1  1 2X  1  X  0 2X+1 2X+1  1  1  0
 0  0  1  0  0  0  1 2X+1  1  1 2X 2X+1 X+1  X  0  1  0  1  2 2X+2  1 X+2 X+2  2  2 2X+1  2 2X+2  X  1  1 2X 2X X+2  2  2  1 2X+2 2X+2 2X+1  0 X+1 2X  2 X+2 X+2 X+1 X+2 X+1  1  2  1 X+1  1 X+1 X+1  X X+2  1  0  1 X+2  X 2X 2X+2  2 2X+1  1  2 2X+1 2X 2X+2 2X+1  X 2X+2  X 2X  0  0 X+2  1  X
 0  0  0  1  0  1  1 2X+2 X+1 X+1 2X+1 X+2 X+1  X  1  2 2X+1  0 2X+2 2X+2  0  1  X  1  X  X X+1  0  2  2 X+2 X+2  2 X+1 2X X+2 X+1 X+2 2X+2  2  X 2X+2  0  1 X+1 2X 2X  0 2X+1 2X+2 2X  X X+1 2X+1 2X+1 2X  2 2X+1 2X+2  2  0  1 X+1 2X+2 2X X+2  0 X+2 2X+2  0  0  1 2X+1  X 2X 2X+1  0 2X  2 X+2  2 2X
 0  0  0  0  1  2  X 2X+2  2  X X+2  2  2 X+2  1 2X+1  1 2X  X  0 2X+2  0 2X+1 X+1 2X  1 2X+1 2X+2 X+1 X+1 2X  0  1  2 2X+1 X+1  1  0 X+1 X+1 2X+1  1 X+1 X+2 X+2  2 2X+1 2X 2X+1  2 2X 2X+1  0  2  2 2X+2  0 X+1 2X X+1 2X+1 2X+1 2X  0 X+2 2X+2 2X+2  2  2 2X+2 X+2  1 2X+2  2  1 2X+2  1  0  X 2X+2 2X X+2
 0  0  0  0  0 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X  X  0  0  X  X 2X  X 2X 2X 2X  X  0  0  X  0  0 2X  X  X 2X 2X 2X  0  X  X  0  0 2X  0 2X  0  X  X  X  X 2X  0 2X 2X 2X  0  0 2X  0  0  X  0  0  X 2X  X 2X  0  X  0  X 2X  X  0  0 2X  X 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+244x^144+186x^145+414x^146+1628x^147+852x^148+846x^149+3208x^150+1650x^151+2076x^152+5606x^153+2724x^154+3030x^155+8770x^156+4014x^157+4470x^158+11468x^159+5004x^160+5370x^161+14484x^162+5724x^163+6108x^164+15294x^165+6090x^166+5958x^167+14330x^168+5226x^169+4938x^170+11050x^171+3936x^172+3372x^173+7210x^174+2460x^175+1800x^176+3390x^177+1050x^178+720x^179+1282x^180+330x^181+198x^182+352x^183+84x^184+48x^185+56x^186+30x^187+18x^188+24x^189+6x^190+8x^192+2x^195+4x^198+2x^201+2x^216

The gray image is a linear code over GF(3) with n=246, k=11 and d=144.
This code was found by Heurico 1.16 in 787 seconds.