The generator matrix

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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 170.

Homogenous weight enumerator: w(x)=1x^0+432x^170+332x^171+750x^173+382x^174+744x^176+348x^177+690x^179+316x^180+522x^182+278x^183+408x^185+132x^186+312x^188+174x^189+168x^191+98x^192+144x^194+72x^195+120x^197+32x^198+72x^200+16x^201+6x^204+12x^206

The gray image is a linear code over GF(3) with n=270, k=8 and d=170.
This code was found by Heurico 1.16 in 53.5 seconds.