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 1 1 1 0 1 1 2X 1 1 1 1 1 X 0 1 X 1 1 1 1 1 0 2X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 0 1 1 1 1 0 1 1 1 2X 1 1 1 1 1 1 1 1 1 1 0 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 0 2X+1 2 X+1 0 2 1 0 X+2 2X+1 1 2 X 1 2X+1 X+2 2X 2X+2 X+1 1 1 X+1 1 0 X+1 2 X X+1 1 1 X+1 2X 2X+2 1 2 2 1 X 0 X+1 2X+1 2X+1 2X 1 1 2X+1 1 2 1 1 2X 2X X+2 1 0 X+1 X+1 1 2X+2 2X+1 1 2X+2 X+2 1 2X+1 2X 0 2X 1 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X 0 X 2X 2X X 2X 0 2X 2X 0 X X 0 2X 2X 0 2X 0 X 2X 0 2X 0 0 2X X 2X X X X 2X 0 2X 0 X X X X 2X X X X X 0 2X 2X 2X 0 0 2X X 0 2X X 0 X 2X 2X 2X 0 2X 2X X 0 2X 0 0 X 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X X 2X 0 2X 0 X X 0 2X 2X 0 2X X 2X 2X 2X 2X X 2X 2X 0 X X 2X 2X 0 2X 2X X 2X X X 2X X 0 X 2X 2X X 2X 2X 2X X 2X 2X 2X 0 2X X X 0 X 2X X 0 0 0 X 0 2X 2X 0 X 2X X 2X 2X 0 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X 0 2X 2X X 2X X 0 0 X X X X 2X X X X 2X 2X X 0 0 2X X 2X X X 0 0 0 0 X 2X X 0 0 0 2X X X 0 2X 2X 2X X X 0 2X X X X 0 X X 2X X 0 0 0 2X 0 2X X 2X 0 2X 2X 2X 0 X 0
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 0 X X X X 2X X 2X 2X 0 2X 0 0 0 2X X 0 2X 2X X 2X X 0 X 0 X 2X X X X X X X X 2X 0 X 2X X X X X 0 X X 2X X X 0 X 2X 2X 0 X X X 0 X 0 2X X 0 0 X 0 X 0 0 0 0
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X X 2X X 0 X X 2X 0 0 2X X 0 X X 0 2X 0 0 X 0 2X X 0 X X 0 0 0 2X 2X 0 0 X 2X X X X 2X X 0 0 X 0 2X 2X X 2X X 2X X 2X 2X 0 0 0 2X 0 0 0 2X 2X 2X X 0 0 0 X 2X X X
generates a code of length 88 over Z3[X]/(X^2) who´s minimum homogenous weight is 156.
Homogenous weight enumerator: w(x)=1x^0+52x^156+24x^157+6x^158+142x^159+72x^160+120x^161+378x^162+138x^163+282x^164+584x^165+240x^166+414x^167+1006x^168+450x^169+396x^170+1422x^171+612x^172+540x^173+1580x^174+654x^175+708x^176+1810x^177+792x^178+612x^179+1546x^180+666x^181+612x^182+1140x^183+414x^184+360x^185+658x^186+198x^187+222x^188+276x^189+96x^190+78x^191+96x^192+18x^193+24x^194+76x^195+48x^198+44x^201+28x^204+26x^207+12x^210+6x^213+2x^216+2x^219
The gray image is a linear code over GF(3) with n=264, k=9 and d=156.
This code was found by Heurico 1.16 in 10.3 seconds.