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

generates a code of length 83 over Z3[X]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+120x^146+386x^147+696x^148+762x^149+1356x^150+1680x^151+1752x^152+2388x^153+3360x^154+3150x^155+4208x^156+4992x^157+4602x^158+5594x^159+7122x^160+6300x^161+7870x^162+9036x^163+7476x^164+8780x^165+10146x^166+8400x^167+8772x^168+9888x^169+7620x^170+7642x^171+8514x^172+5556x^173+6004x^174+5454x^175+3816x^176+3490x^177+3024x^178+1992x^179+1636x^180+1338x^181+702x^182+700x^183+312x^184+186x^185+166x^186+48x^187+48x^188+34x^189+6x^191+10x^192+6x^195+2x^198+2x^204+2x^207

The gray image is a linear code over GF(3) with n=249, k=11 and d=146.
This code was found by Heurico 1.16 in 672 seconds.