The generator matrix

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

generates a code of length 97 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+50x^168+226x^171+314x^174+6x^175+362x^177+96x^178+472x^180+246x^181+456x^183+648x^184+486x^186+1344x^187+462x^189+2064x^190+442x^192+2316x^193+448x^195+2586x^196+490x^198+2154x^199+470x^201+1068x^202+434x^204+510x^205+362x^207+72x^208+334x^210+12x^211+270x^213+172x^216+126x^219+94x^222+50x^225+18x^228+12x^231+4x^234+4x^240+2x^243

The gray image is a linear code over GF(3) with n=291, k=9 and d=168.
This code was found by Heurico 1.16 in 19.9 seconds.