The generator matrix

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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+68x^168+174x^169+354x^170+914x^171+1488x^172+1362x^173+2064x^174+3360x^175+2448x^176+3944x^177+5880x^178+3528x^179+5276x^180+6996x^181+3942x^182+4806x^183+5022x^184+2118x^185+2024x^186+1410x^187+606x^188+342x^189+282x^190+108x^191+92x^192+114x^193+54x^194+88x^195+24x^196+30x^197+28x^198+18x^199+24x^200+20x^201+18x^202+6x^203+12x^204+2x^213+2x^228

The gray image is a linear code over GF(3) with n=810, k=10 and d=504.
This code was found by Heurico 1.16 in 14.1 seconds.