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 0 1 1 1 1 1 X 0 X 1 1 0 1 1 1 1 0 X 2X 1 1 1 1 X X 1 1 1 1 1 1 0 2X 1 1 1 1 0 X 1 1 1 1 1 2X 1 1 2X 2X 1 1 1 1 1 1 1 1 2X 1 1 1 1 1 1 1 0 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 1 2X X+2 2X 2X X+2 0 1 1 1 1 1 0 2X 2X+1 X+1 1 2X 1 0 X 1 2 1 1 1 X+2 2 1 2 X 1 1 2X 2X X+2 X+1 1 X X+1 2X 2 X X+1 1 2 2 1 2X 2X+1 X+1 0 0 X X+1 1 2X 2X 2X+2 2X+1 2X+1 0 2 X 2 1 2X+2 0 2X X+2 2X+2 2 X+1 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 0 2X X+1 X X+2 2X 1 X+1 2X 2X X+1 X 1 X 2X+2 0 2 1 2X+2 2X+2 2 X+1 0 0 1 0 X+1 X+2 2X+2 2X 1 2 X+1 0 2X+2 X+1 X+2 2X 1 X 2X+1 X+2 X X+1 2 2 2X+2 2X+1 1 X+2 2X 2X 2X+2 1 X+2 X+1 2X 1 2X+1 1 2X+2 1 0 X+2 2X+2 0 X+2 2X+2 1 1 X+2 X 0 1 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 X 2X 2X X 2X X 2X X X X 2X 0 X 0 X 0 2X X 0 0 2X 2X X 0 X 2X 0 0 X 0 2X 2X 2X 2X 2X 0 X 2X X 2X 0 2X X X X X 2X 2X 0 0 X X 2X 0 2X X 0 0 0 0 0 0 2X X 0 X 0 2X 2X 0 X 2X 2X X 0
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 2X X X 0 X 2X X X X X 0 X X X X 0 0 0 2X 2X 2X X 2X X X X 0 2X X 0 2X 0 0 2X 2X X 2X 0 X X 0 0 X X 0 0 2X 0 2X X 0 2X X X 2X 0 0 0 0 X 2X X X 2X X X X 0 X
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 X X 0 0 2X 2X 2X 2X X X 0 2X 0 X 2X 0 2X X 0 0 X X 2X 2X 2X 2X 2X 2X X 0 X X 2X X X 0 0 0 0 0 2X 2X X 2X 2X 0 0 X X X 2X X 2X X X 0 X 0 X X X X 0 2X X X 2X
0 0 0 0 0 0 X X X X 0 0 2X X 0 2X 2X 2X X 0 2X X 2X 0 2X X X 2X X X 0 X 2X 2X 0 2X 2X 0 0 X 0 X 0 X 0 0 X 2X 2X 2X 2X X 0 2X 0 0 0 0 X X 2X X 2X 0 2X X X 2X 2X X 0 0 X 0 X 2X 0 2X 2X 2X 2X X 0 0 0 X 2X 2X 2X 0 2X 0 2X 0 2X 0 X 2X 2X
generates a code of length 99 over Z3[X]/(X^2) who´s minimum homogenous weight is 177.
Homogenous weight enumerator: w(x)=1x^0+90x^177+24x^178+102x^179+506x^180+252x^181+342x^182+1248x^183+426x^184+606x^185+1826x^186+882x^187+990x^188+2764x^189+1290x^190+1218x^191+3208x^192+1452x^193+1650x^194+3978x^195+1878x^196+1848x^197+4684x^198+1830x^199+1932x^200+4672x^201+1728x^202+1608x^203+4138x^204+1512x^205+1278x^206+2654x^207+930x^208+888x^209+1466x^210+600x^211+390x^212+946x^213+240x^214+210x^215+336x^216+72x^217+48x^218+128x^219+6x^220+12x^221+60x^222+32x^225+20x^228+26x^231+8x^234+4x^237+6x^240+4x^243
The gray image is a linear code over GF(3) with n=297, k=10 and d=177.
This code was found by Heurico 1.16 in 83.1 seconds.