The generator matrix

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

generates a code of length 97 over Z3[X]/(X^2) who´s minimum homogenous weight is 173.

Homogenous weight enumerator: w(x)=1x^0+174x^173+260x^174+744x^175+954x^176+972x^177+1722x^178+2424x^179+1872x^180+2982x^181+3450x^182+3034x^183+4614x^184+5004x^185+4010x^186+6768x^187+6816x^188+5428x^189+7710x^190+8694x^191+5974x^192+9228x^193+9192x^194+6264x^195+9408x^196+9144x^197+6206x^198+7932x^199+7998x^200+4770x^201+6570x^202+5730x^203+3672x^204+4398x^205+3432x^206+2028x^207+2292x^208+1740x^209+1030x^210+870x^211+606x^212+230x^213+276x^214+216x^215+120x^216+90x^217+30x^218+30x^219+6x^220+6x^221+4x^222+12x^225+2x^228+4x^231+2x^234+2x^237

The gray image is a linear code over GF(3) with n=291, k=11 and d=173.
This code was found by Heurico 1.16 in 829 seconds.