The generator matrix

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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+68x^159+72x^161+438x^162+150x^163+246x^164+1092x^165+534x^166+612x^167+1962x^168+816x^169+1068x^170+2500x^171+1062x^172+1224x^173+3342x^174+1572x^175+1614x^176+4240x^177+1902x^178+1902x^179+4808x^180+2106x^181+1902x^182+4850x^183+1860x^184+1650x^185+3924x^186+1488x^187+1506x^188+2626x^189+876x^190+828x^191+1644x^192+570x^193+318x^194+754x^195+168x^196+150x^197+304x^198+18x^199+12x^200+106x^201+18x^203+52x^204+32x^207+28x^210+12x^213+8x^216+6x^219+4x^222+2x^225+2x^228

The gray image is a linear code over GF(3) with n=270, k=10 and d=159.
This code was found by Heurico 1.16 in 73.6 seconds.