The generator matrix

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

generates a code of length 98 over Z3[X]/(X^2) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+234x^178+396x^179+394x^180+636x^181+1020x^182+856x^183+1338x^184+1542x^185+1350x^186+2058x^187+2106x^188+1418x^189+2466x^190+2550x^191+1956x^192+2760x^193+2670x^194+2058x^195+2694x^196+2976x^197+1940x^198+3126x^199+2886x^200+1964x^201+2442x^202+2322x^203+1434x^204+1956x^205+1722x^206+1096x^207+1260x^208+972x^209+492x^210+630x^211+462x^212+216x^213+180x^214+198x^215+86x^216+72x^217+24x^218+14x^219+12x^220+24x^221+12x^222+6x^223+2x^225+6x^228+6x^231+2x^234+4x^237+2x^243

The gray image is a linear code over GF(3) with n=294, k=10 and d=178.
This code was found by Heurico 1.16 in 96.5 seconds.