The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 1 0 2X 1 1 1 1 1 1 0 1 1 1 2X 1 1 1 0 1 1 1 2X 1 1 0 X 1 1 1 1 1 1 X 1 1 0 1 1 1 1 1 X 1 1 1 1 1 X 2X 1 1 0 2X 1 1 1 1 1 1 X X 1 1 1 2X
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 0 2X+1 2 2X+2 X+1 X 1 1 0 2X+1 2 X 2 1 1 2 2X 2X+1 1 X+2 2X 1 1 1 0 1 1 2 2X+2 1 1 2X 2X+1 X+2 2X+2 2X+2 2X 1 2X+1 2X+1 1 1 X+2 X+2 X X+2 1 X 2X X+1 1 0 1 1 0 X 1 1 2X+1 0 X+2 2 1 X 1 1 1 X+1 2 1
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X 2X X 2X X X X X 2X 2X 2X 2X 0 2X 0 X X X X X X 2X 0 2X 2X X 0 2X X 2X 2X 0 0 2X X X X X 2X X X X 0 2X 0 0 2X 0 0 X 2X 2X 0 2X 0 2X X X X 0 0 2X 2X X X 2X 2X 2X X X
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 2X 2X X X 0 X 0 X 2X X 0 2X X X 2X X X 0 X 2X 0 2X 0 2X 0 X X X 0 X X X X 0 0 X X 2X 0 0 X X 0 X X 2X X 0 2X X 0 X X 0 2X X 2X 2X X X 2X X X 2X 0 0 X X 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X X 2X X X 2X 0 X 2X 0 2X X 2X X 2X X 0 2X X X 0 0 2X X 0 0 2X 0 X 2X 0 0 2X 2X 0 X 2X 0 0 0 2X 0 X 2X 2X X 0 X 0 0 0 0 2X 2X 0 2X 2X 2X X X 2X X 0 X X 0 2X 0 2X X 2X 2X 0
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 0 X 0 2X 2X 0 2X 2X 0 0 0 X 2X 0 X 0 2X X 0 X X X 2X 0 2X X 2X X 0 2X 0 2X 0 2X 0 0 X X 2X 2X X 0 X X 0 X 2X 2X 2X 2X 0 2X X 0 2X X 2X 2X X 2X 2X 0 2X 2X X 2X 0 2X 0 0 2X X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 0 2X X 0 X 0 2X 0 X X X X X 0 X X 0 X 2X 0 X X X X 0 X 0 2X 0 2X X X 0 X 2X 2X 0 2X X 2X 0 2X 0 0 2X X 2X 0 2X 2X X 0 2X 2X 2X 0 0 0 0 X 2X 2X X X X 2X 0 0 0 0 0 0
generates a code of length 87 over Z3[X]/(X^2) who´s minimum homogenous weight is 156.
Homogenous weight enumerator: w(x)=1x^0+130x^156+18x^157+54x^158+294x^159+150x^160+180x^161+600x^162+204x^163+306x^164+978x^165+360x^166+402x^167+1168x^168+558x^169+582x^170+1478x^171+780x^172+720x^173+1636x^174+666x^175+744x^176+1618x^177+702x^178+582x^179+1328x^180+492x^181+504x^182+906x^183+306x^184+204x^185+326x^186+102x^187+60x^188+178x^189+36x^190+36x^191+96x^192+66x^195+48x^198+26x^201+36x^204+12x^207+8x^210+2x^213
The gray image is a linear code over GF(3) with n=261, k=9 and d=156.
This code was found by Heurico 1.16 in 14.1 seconds.