The generator matrix
1 0 0 1 1 1 1 1 0 2X 1 1 1 1 1 0 1 1 1 1 1 1 2X X 1 0 1 1 1 1 1 1 0 2X X 1 1 1 1 1 1 1 X 2X 1 1 1 2X X 2X 1 1 2X 1 0 1 0 1 1 0 1 1 1 1 X 0 1 1 1 1 1 1 0 2X X X 1 1 1 1 1 X 1 1 1 1 1 1
0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 2X 1 2X 0 X+1 2X+2 1 2 2 1 1 2X 1 X+2 2X 2X X+2 2X+1 2X+1 1 2X 1 X+2 2 2X+1 X X 2X 1 1 1 2 X 2X+1 2X 1 1 1 2X+2 1 2 1 X+1 2X X 0 1 X+2 X+1 2X+2 0 0 1 X 1 2X 2X+1 2X+2 X+1 2X 1 X 1 2 1 2 2X+1 2X+2 X 2 X+1 2X 0 2X+1 0
0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 2X+1 1 1 X+2 2 X+1 0 X 2 2 1 2X 0 X+1 X X+2 2X X 1 X 1 2 X+2 2 X+2 X+2 2X 2X+1 X+1 2X+2 0 1 1 2 1 X+2 2X+1 2X+1 0 2 X+1 1 X+1 1 1 X+1 2 X+1 2X 1 1 1 X+2 X+2 2X+1 X+2 X+2 X+1 1 1 X 1 2X+2 X+2 2X 2X+2 0 0 1 1 2X X+2 2X+1 2X+2 0
0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 0 0 2X 2X 2X 2X X 2X X 2X X 2X X 2X X X 2X 0 2X 2X 2X 0 2X 0 X 0 0 2X 2X 0 2X X 0 X 2X 2X 2X 0 2X 2X X 2X X 2X 2X X 0 0 0 0 X 0 2X X 2X 2X X X 2X 2X X 0 0 X 0 0 2X X 0 0 2X 2X X
0 0 0 0 2X 0 0 0 0 0 X 2X 0 2X 0 0 X 0 0 X 2X 0 X 2X 2X 2X X X 2X 2X 0 2X 2X 2X X 0 X 2X 2X 2X 2X X 0 2X 2X X 2X 0 0 2X 2X X X 0 X 0 2X X X 2X X X 2X X X 0 X X 2X X 2X 2X X 0 2X 2X X 2X 0 2X 0 X 0 X 2X 0 0 2X
0 0 0 0 0 X 0 X X 2X X 2X 2X 2X X X 2X X 0 2X 2X 0 0 0 X X 0 0 0 2X 2X 0 0 2X 2X 2X X 2X 2X 0 0 X 0 X 2X 2X 2X X 2X 2X 0 X 0 X X X X 2X 0 X 2X 2X 0 2X 0 0 0 X 0 0 X X 0 0 0 2X X 0 2X 2X 2X 2X X 2X 2X X X X
0 0 0 0 0 0 X X X X 0 0 2X X 0 2X 2X 2X X 0 2X X 2X 0 X 2X X 2X X X X 0 2X 0 2X X 2X 0 0 X 2X 2X 2X 2X X 0 X X X 2X X 0 0 X X X X X 0 0 2X 2X X X X 2X 2X X X 0 2X 0 0 0 2X 2X 0 X 0 X 0 X 0 X X 2X 0 0
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+76x^156+78x^157+180x^158+178x^159+564x^160+882x^161+324x^162+1140x^163+1374x^164+364x^165+1848x^166+2034x^167+622x^168+2532x^169+2856x^170+690x^171+3240x^172+3594x^173+796x^174+4038x^175+3930x^176+1008x^177+4182x^178+3606x^179+924x^180+3516x^181+3552x^182+646x^183+2556x^184+2274x^185+350x^186+1566x^187+1212x^188+236x^189+684x^190+540x^191+120x^192+228x^193+168x^194+68x^195+66x^196+30x^197+42x^198+6x^199+12x^200+42x^201+32x^204+24x^207+8x^210+8x^213+2x^222
The gray image is a linear code over GF(3) with n=264, k=10 and d=156.
This code was found by Heurico 1.16 in 71.9 seconds.