The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 X 1 1 1 0 1 1 X 1 1 1 1 0 1 1 2X 1 0 1 1 1 1 1 X 1 X 1 1 2X 2X 1 2X 1 1 1 1 1 1 1 1 1 1 2X 1 2X 2X 1 0 1 1 1 1 1 0 1 1 1 0 1 1 2X 1 1 1 1 1 1 1 1 1 X 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 0 X+1 1 0 1 2X+1 2 X+2 1 2X+1 0 1 0 2X+1 X+2 X+1 1 2 1 1 X 1 2 2X 2X+2 1 2X 1 1 1 2X+2 2 1 1 2X+2 1 X+1 2X+2 X+2 X 2X+1 2 X+1 1 X X 1 0 1 1 2X+2 1 2 2X+1 X+2 X 1 1 2X+2 X 0 1 X 2X 1 X+1 2X+2 2X+1 2X+1 X+2 2X 2X+2 2X 0 1 0 X+2
0 0 2X 0 0 0 0 0 0 0 2X X X X X 0 2X 0 2X X X X 0 0 X 0 2X 2X X 2X 2X 2X 0 X X 2X X 0 2X X 2X 2X 2X 0 0 2X 2X 0 2X 0 2X X X X 0 0 X X X 2X X 0 2X 0 2X X 2X 0 X X X 2X 2X 0 0 2X 0 0 X 0 2X 0 X 0 0 0 2X X X 2X
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X X 2X X 2X 2X 0 X 2X 2X 0 0 X 0 2X 0 0 0 2X 0 2X 2X 0 2X 2X 2X X X 2X 0 X 0 X 0 2X X 2X X X X 2X 0 2X X 2X 2X 2X 2X 0 2X X 0 X 0 0 2X X 0 X 2X 2X 2X 0 X X X 2X 0 X 2X 0 2X X X 2X X
0 0 0 0 X 0 X X X X X 2X 0 0 X 0 X 2X 0 2X X X 2X 2X X X X X 0 X 0 0 2X 0 2X 0 X 0 X 2X 2X X X 2X 2X X 2X 0 2X 0 0 X X 0 0 X X X X 0 2X X 0 X 0 0 2X 2X 2X X X 0 2X X 0 0 0 2X X 2X 2X 2X 2X 0 X 0 X 0 X 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X 2X X 2X 2X 2X 0 X 2X 0 X 0 X X 0 2X 0 X X 2X 2X X X X 0 2X X X 0 X 0 2X 0 2X X 0 X 2X 2X X 0 0 0 2X 0 2X 2X X 0 0 2X X X 0 2X 0 2X 2X X 0 0 X 0 2X 2X 0 X X X X 0 0 X X X 0 0 X
generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 167.
Homogenous weight enumerator: w(x)=1x^0+108x^167+210x^168+432x^170+250x^171+480x^173+284x^174+606x^176+308x^177+666x^179+258x^180+654x^182+260x^183+636x^185+224x^186+462x^188+176x^189+216x^191+76x^192+108x^194+46x^195+6x^197+30x^198+22x^201+16x^204+6x^207+4x^210+4x^213+6x^216+2x^219+2x^222+2x^225
The gray image is a linear code over GF(3) with n=270, k=8 and d=167.
This code was found by Heurico 1.16 in 2.89 seconds.