The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 X 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 2X 1 X 1 1 1 0 1 1 1 1 2X 1 X 1 X 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 2X 1 1 2X 1 1 X X 0 1 1 1 1 1 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 2X+1 0 2 1 2X+1 X+2 0 1 2 2X+1 X 1 1 2X+1 X+2 0 2 1 0 2X+1 2 X+2 X X+1 2X+1 0 1 X+2 1 X X 2X+1 1 X+2 1 X+2 X 1 1 1 0 1 1 0 2X+2 2X X+2 2 2X 2X+1 1 X+1 2X 1 2 2X 2X 1 X+2 2X 1 2 X+2 2X 0 1 2X+1 2 X+1 2X 0 X X+2 X+2 X+2 0
0 0 2X 0 0 0 0 0 0 2X X 0 X X 2X X 0 2X 2X 2X X 2X X X 0 0 X 2X 2X X 0 0 0 X X X 2X 2X X X 0 2X 0 2X 0 2X X X X X 2X X 2X 0 X X X 2X 2X 2X X 0 2X 0 X X 2X 2X X X 2X X X 2X X X 0 X 2X X X 2X X 0 X X 2X 0 0 0 2X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X X 2X 2X X 2X X X 2X X 2X X 0 0 X X 0 X 2X 0 2X 2X 0 X 0 X 2X 0 0 X 2X 2X X 2X 0 2X X X X 2X X 0 0 X 2X 0 2X 0 X 0 2X 2X 2X X X X X 0 2X X 2X X 0 0 X X X X 0 0 X X X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 2X X X X 2X 2X 2X X 0 X X X 2X 2X 2X X 2X 2X 2X 2X X 2X X 2X 2X 0 X 2X X X X 0 X 2X 0 0 X X 0 X 2X 2X 2X X X 0 X 2X 2X 2X X X X 0 X X 0 0 2X X X 2X 2X X X X 2X X 2X
0 0 0 0 0 2X 0 0 0 0 0 2X 0 X 0 0 0 X X 0 X X X 2X 0 2X 2X 2X 2X 2X 2X X X 2X X X 0 X 0 X X 0 0 X 0 X 2X 0 X X 0 0 2X 0 2X X X X X 2X X 0 X 2X 2X 0 2X X 2X 0 0 2X 0 0 X 2X X X 2X X 2X 2X 0 X X 2X 0 0 2X 2X 0 X
0 0 0 0 0 0 X 0 2X 2X X 0 0 2X 2X 2X X 0 2X X 0 0 2X 2X 2X 0 0 X X 2X 0 X 0 0 X X 0 2X X X X X X 0 0 X 0 2X 0 2X 2X 2X 0 2X X 0 0 X X 0 0 2X 0 X X 2X X X 2X X 2X 2X X 0 0 X X 0 X X 0 0 2X X 0 2X 2X X 2X 0 2X 2X
0 0 0 0 0 0 0 X X 2X 0 X 2X X X X X 2X X 0 X X 2X 0 0 2X 0 X X X 2X X 0 X 2X X 2X 0 2X 0 0 0 0 2X X X 2X 2X 0 X 0 0 0 0 2X X 2X 2X X 2X 0 2X 2X 0 X 2X 0 0 X 2X 0 2X 2X 0 2X 0 2X 2X 2X 0 X 2X X 2X 2X X X 2X 2X X 2X 0
generates a code of length 92 over Z3[X]/(X^2) who´s minimum homogenous weight is 159.
Homogenous weight enumerator: w(x)=1x^0+78x^159+6x^161+250x^162+60x^163+78x^164+336x^165+186x^166+312x^167+390x^168+474x^169+750x^170+456x^171+1176x^172+1332x^173+496x^174+1956x^175+2406x^176+476x^177+2904x^178+3276x^179+478x^180+3702x^181+3816x^182+506x^183+4500x^184+4260x^185+450x^186+4326x^187+4122x^188+456x^189+3318x^190+3054x^191+422x^192+2172x^193+1680x^194+470x^195+1008x^196+750x^197+406x^198+330x^199+306x^200+280x^201+96x^202+90x^203+212x^204+36x^205+6x^206+168x^207+98x^210+82x^213+26x^216+20x^219+2x^222+2x^228
The gray image is a linear code over GF(3) with n=276, k=10 and d=159.
This code was found by Heurico 1.16 in 89.1 seconds.