The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 1 0 1 1 1 1 X 1 1 X 1 1 1 2X 1 1 0 1 1 X 1 X 1 1 1 1 1 1 1 1 X 1 1 1 1 2X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 0 0 1 X 1 1 1 1 1 X 1 X 0 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 2X+1 0 1 2 2X+1 2 X 1 1 2X 1 X+2 2X 2X+1 1 2X+1 X 1 1 2X 1 2 1 0 2X+1 2X+2 X+1 2X+2 X X+2 0 1 X+1 2X 0 X+1 1 2X+1 X 2X+2 2X+2 1 X+2 1 2X 1 1 X+2 2X 1 1 1 2X+1 1 1 1 2X+1 1 1 1 X+2 1 X+1 2X 0 X+1 X+1 1 2X+1 1 1 0
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 2X X 0 2X X 2X 0 X X 2X X 2X 0 0 X X X X 0 X X 2X 2X 2X X 2X X 2X 0 X 0 X X X 2X 2X 2X 0 X 0 2X 0 0 0 0 2X 0 X 0 2X 2X 0 X 0 X X 0 X 0 2X 2X X 2X 0 2X 0 2X 0 X 0 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 0 2X 2X 2X X X 0 X 0 X 0 2X X 2X 0 2X X X X X 2X 2X 2X X X 0 X 0 X X 0 2X 2X 2X 0 0 X 0 X 0 X 0 0 X X 0 X X 0 X 2X X X X X 0 0 X X 2X 0 0 X 0 0 2X 2X 0 X 2X 2X 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 X 0 0 X 2X 2X 2X 2X X 2X 0 X X X 2X 2X X 0 2X X 0 0 2X 0 2X X 2X 2X 2X 0 2X X 0 X X 0 2X 0 X X X 0 0 X X 0 0 0 2X 2X 2X X 0 X 2X 0 2X 2X 0 2X 2X 0 X 0 2X 2X 0 X 2X 0 X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 0 0 X 0 0 2X 2X 2X 2X 2X X X X 2X X X 0 2X X 0 2X 0 0 0 0 2X 2X X 0 X X X X 2X 0 0 X 2X X X X 0 0 2X 0 2X X 2X 0 2X 2X 0 0 2X 2X X X 2X X 2X X X 2X X X 0 X 2X X 2X X
generates a code of length 91 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.
Homogenous weight enumerator: w(x)=1x^0+76x^168+6x^169+78x^170+320x^171+120x^172+222x^173+438x^174+174x^175+198x^176+454x^177+204x^178+198x^179+518x^180+258x^181+168x^182+492x^183+258x^184+180x^185+480x^186+216x^187+144x^188+404x^189+162x^190+78x^191+244x^192+54x^193+108x^194+114x^195+6x^196+66x^197+28x^198+18x^200+24x^201+10x^204+10x^207+6x^210+14x^213+6x^216+2x^219+4x^222
The gray image is a linear code over GF(3) with n=273, k=8 and d=168.
This code was found by Heurico 1.16 in 1.16 seconds.