The generator matrix

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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+96x^169+240x^170+232x^171+408x^172+432x^173+314x^174+456x^175+366x^176+316x^177+348x^178+396x^179+238x^180+366x^181+288x^182+168x^183+234x^184+240x^185+176x^186+162x^187+198x^188+66x^189+132x^190+114x^191+80x^192+144x^193+66x^194+48x^195+30x^196+30x^197+36x^198+12x^199+48x^200+8x^201+30x^202+12x^203+12x^204+12x^205+6x^207

The gray image is a linear code over GF(3) with n=270, k=8 and d=169.
This code was found by Heurico 1.16 in 0.969 seconds.