The generator matrix

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

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+156x^178+342x^179+426x^180+690x^181+966x^182+818x^183+1440x^184+1728x^185+1334x^186+2124x^187+1896x^188+1450x^189+2424x^190+2730x^191+1984x^192+2466x^193+2832x^194+2046x^195+3198x^196+2850x^197+1856x^198+2748x^199+2880x^200+1874x^201+2454x^202+2172x^203+1564x^204+1884x^205+1650x^206+1064x^207+1326x^208+1032x^209+562x^210+654x^211+618x^212+254x^213+216x^214+138x^215+54x^216+66x^217+24x^218+14x^219+24x^220+12x^221+4x^222+4x^228

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 83.9 seconds.