The generator matrix

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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+164x^162+168x^163+576x^164+646x^165+492x^166+1368x^167+1242x^168+954x^169+2112x^170+1508x^171+1278x^172+2592x^173+2148x^174+1638x^175+3162x^176+2578x^177+1770x^178+3726x^179+2822x^180+1680x^181+3720x^182+2754x^183+1788x^184+3384x^185+2262x^186+1428x^187+2676x^188+1918x^189+990x^190+1806x^191+1010x^192+612x^193+768x^194+422x^195+222x^196+288x^197+136x^198+96x^199+54x^200+22x^201+6x^202+12x^203+24x^204+6x^207+6x^210+4x^213+4x^216+2x^222+2x^225+2x^228

The gray image is a linear code over GF(3) with n=270, k=10 and d=162.
This code was found by Heurico 1.16 in 75.5 seconds.