The generator matrix

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

generates a code of length 93 over Z3[X]/(X^3) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+344x^174+636x^175+1338x^176+3154x^177+4218x^178+5406x^179+6962x^180+8358x^181+9366x^182+11482x^183+13338x^184+14244x^185+15002x^186+15822x^187+14190x^188+14444x^189+11064x^190+8742x^191+6454x^192+5046x^193+3078x^194+2082x^195+1116x^196+354x^197+340x^198+126x^199+84x^200+156x^201+24x^202+36x^203+48x^204+12x^205+12x^206+24x^207+18x^208+6x^209+14x^210+6x^212

The gray image is a linear code over GF(3) with n=837, k=11 and d=522.
This code was found by Heurico 1.16 in 102 seconds.