The generator matrix

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

generates a code of length 91 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+1184x^171+1350x^172+1890x^173+4950x^174+5184x^175+5184x^176+10872x^177+10350x^178+9072x^179+16212x^180+14166x^181+11754x^182+18312x^183+14274x^184+10998x^185+14238x^186+9450x^187+4914x^188+5882x^189+3168x^190+1260x^191+1350x^192+360x^193+126x^194+324x^195+18x^196+160x^198+102x^201+36x^204+6x^207

The gray image is a linear code over GF(3) with n=819, k=11 and d=513.
This code was found by Heurico 1.16 in 130 seconds.