The generator matrix

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

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+234x^169+306x^170+70x^171+462x^172+474x^173+154x^174+384x^175+522x^176+122x^177+462x^178+366x^179+108x^180+384x^181+384x^182+106x^183+318x^184+294x^185+66x^186+228x^187+240x^188+28x^189+162x^190+132x^191+40x^192+162x^193+96x^194+6x^195+66x^196+60x^197+16x^198+36x^199+36x^200+6x^201+18x^202+6x^203+4x^204+2x^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 8.42 seconds.