The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 X 1 1 1 0 1 1 1 X 1 1 1 2X 1 1 1 1 1 0 1 1 1 1 1 2X 1 0 1 0 1 1 X 1 1 0 1 0 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 2X 2X 1 1 0 1 1 1 0 2X 1 1 X 1 0 X 2X 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 X 2 2X+1 1 2 2X+1 0 1 2X+1 2 2X 1 X+1 2 0 1 0 X+2 X+1 2X 1 1 X+2 0 2X+1 X+2 0 1 2X 1 2X+1 1 2X+1 2 1 X 2X+2 1 X+1 1 X+2 2X 2 0 X+2 2X 2 0 2X+1 1 1 X+2 2 X+2 2X 2X 2 1 2X+2 X+1 1 1 2X+2 X+1 1 0 X+1 2X 1 1 0 2X+1 1 X+1 1 1 1 2X+1 2X+1 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X 0 X 2X X X X 0 2X 0 2X 0 2X X X 0 2X 2X X 2X 2X 0 X 2X X 2X 2X 2X 0 X 0 2X X 0 2X 2X 2X 0 2X X X 2X X 2X 0 2X 0 2X 2X X 2X X X 2X 0 2X X 2X 2X X 2X 0 2X 0 0 X 0 2X X 0 X X 2X 0 2X 2X 0 X 0 0 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 2X X 0 X X 2X X 2X X X 0 2X X X X 0 X 0 X X 2X X X 0 0 0 2X 2X 2X 0 X 2X 2X X 2X 2X 0 0 X 0 0 2X X X 0 2X 2X 0 0 2X X X X 2X X 0 2X 0 X X 0 0 2X X X 2X 2X 0 0 X 0 X 0 2X 0 2X 0 X 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X X X 0 2X 0 X X 2X 0 X X 2X 2X 2X X 0 0 X 0 X X 2X X X 2X 2X 2X 0 2X 0 2X 0 X 0 X 0 X 0 2X 0 0 X X 2X X 0 0 X 2X X 2X X 0 X 2X X 2X 2X 2X X 0 X X X X 2X X 0 2X X 0 2X X 2X X X 2X X X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X X X 0 0 X X 0 2X X 0 X X 2X 0 X 0 X 2X 2X 0 0 X 2X 0 0 0 0 2X X 2X 2X 0 0 2X 2X X 0 0 X 2X X 2X 0 2X 0 0 2X X 0 2X 2X 2X 0 X 2X 0 X 2X 2X X 0 X X 0 X X 2X 0 0 2X 0 0 0 2X 0 0 2X X X X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X 2X 0 2X 0 0 0 2X 0 0 2X X 0 2X X X 2X X 0 X 2X 2X 2X 0 0 0 2X 2X 2X 0 2X 2X 2X 0 2X 0 X X 2X 2X 0 2X 2X 0 2X X X 2X 2X 0 2X 0 2X 0 X X 0 X 0 2X 0 0 0 2X 2X 0 0 X X 2X 2X 2X X 2X 0 X X X 2X X
generates a code of length 97 over Z3[X]/(X^2) who´s minimum homogenous weight is 174.
Homogenous weight enumerator: w(x)=1x^0+36x^174+6x^175+48x^176+176x^177+150x^178+180x^179+214x^180+324x^181+456x^182+194x^183+654x^184+672x^185+228x^186+846x^187+1008x^188+184x^189+1176x^190+1098x^191+148x^192+1302x^193+1440x^194+168x^195+1428x^196+1386x^197+150x^198+1212x^199+1242x^200+118x^201+918x^202+744x^203+120x^204+486x^205+342x^206+100x^207+204x^208+120x^209+94x^210+36x^211+12x^212+74x^213+6x^214+54x^216+40x^219+32x^222+20x^225+16x^228+6x^231+6x^234+2x^237+6x^240
The gray image is a linear code over GF(3) with n=291, k=9 and d=174.
This code was found by Heurico 1.16 in 11.6 seconds.