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

generates a code of length 93 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+26x^171+48x^172+48x^173+106x^174+258x^175+228x^176+152x^177+420x^178+492x^179+610x^180+306x^181+1182x^182+2138x^183+384x^184+1998x^185+3272x^186+396x^187+1890x^188+2598x^189+342x^190+1008x^191+390x^192+378x^193+258x^194+38x^195+192x^196+150x^197+42x^198+108x^199+30x^200+32x^201+60x^202+20x^204+18x^205+6x^206+16x^207+6x^208+8x^210+6x^213+10x^216+6x^219+4x^231+2x^237

The gray image is a linear code over GF(3) with n=837, k=9 and d=513.
This code was found by Heurico 1.16 in 3.81 seconds.