The generator matrix

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

generates a code of length 97 over Z3[X]/(X^2) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+152x^174+360x^176+520x^177+1236x^179+884x^180+2106x^182+1240x^183+3246x^185+1740x^186+4554x^188+2262x^189+5064x^191+2476x^192+5592x^194+2632x^195+5736x^197+2740x^198+4638x^200+1964x^201+3468x^203+1476x^204+2016x^206+740x^207+984x^209+482x^210+294x^212+156x^213+66x^215+72x^216+6x^218+46x^219+50x^222+18x^225+10x^228+14x^231+6x^234+2x^237

The gray image is a linear code over GF(3) with n=291, k=10 and d=174.
This code was found by Heurico 1.16 in 81.4 seconds.