The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 X 1 1 1 0 1 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 X 1 2X 1 1 1 X 1 X 1 1 1 1 1 1 1 2X 0 0 1 2X 1 1 1 1 2X 1 X 1 1 1 1 1 1 X 1 1 1 1 2X 1 1 2X 2X 1 2X 1 1 1 0 1 1 0
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 X+1 0 1 0 1 2X+1 2 X+2 1 2X+1 0 1 2X+1 0 2 X+1 2X+2 1 X 2X+1 2X+1 X+2 X X+2 2 2X+2 2X+1 1 2 1 X 1 X+1 1 2X 1 2X+1 2 X 2X+2 2X 2X 1 1 1 1 2X 1 2 1 1 2X+2 1 2X+1 1 2X X+1 X+1 1 1 1 1 2 X+1 X X 1 2X+1 2X+2 1 1 X+2 1 2 X+2 X+2 1 2X+2 2 1
0 0 2X 0 0 0 0 0 0 0 2X X X X X 0 2X 0 2X X X X 0 0 X 2X 0 2X 2X 0 X 2X 2X 2X X X 2X X 0 X 2X 0 0 X X X X 0 2X 2X 0 2X 2X 0 2X X X 0 X 2X 2X 0 X 2X X X X X X 0 0 2X X X 2X X 2X 2X 2X 2X X 2X 0 0 X X X 2X 0 2X 2X X 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X X 2X X 2X 2X 0 X 2X 0 0 X 2X 0 2X X 2X 0 0 2X 0 2X X 2X 0 X 2X 2X 0 X X X 0 0 0 X 0 X 0 X 2X 2X 2X 2X 2X 0 X 2X 0 0 X X 2X 0 2X 2X 0 X X X 0 X 2X 0 X 2X 2X 0 2X X 2X X 0 X 2X 2X 0 0 2X
0 0 0 0 X 0 X X X X X 2X 0 X 0 0 X 2X 0 2X X X 2X X X X 2X 0 X 2X 2X X 0 0 X X 0 0 0 0 X 0 X X 0 X 2X 0 X X 2X 2X 2X 0 2X 0 X 0 0 2X 2X X X 2X X 0 X 2X 2X 2X X 2X 0 X 0 2X X 0 X 2X 2X X 2X X 0 X X 0 X 2X 2X 2X 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X 2X 2X 0 X 2X 0 X X X 0 0 X X 0 X 2X 2X X X 2X 0 X 0 0 0 2X 2X 2X X X 0 2X X X 2X X 0 X 0 2X 0 0 X X X 0 0 0 2X X 0 X X 2X 0 2X 2X 0 0 X 0 X 0 X 2X X X 2X 2X X 2X 2X 2X 2X 2X X 0
generates a code of length 93 over Z3[X]/(X^2) who´s minimum homogenous weight is 172.
Homogenous weight enumerator: w(x)=1x^0+66x^172+138x^174+372x^175+268x^177+486x^178+282x^180+582x^181+308x^183+564x^184+356x^186+642x^187+292x^189+558x^190+196x^192+576x^193+198x^195+366x^196+54x^198+90x^199+20x^201+54x^202+14x^204+18x^205+14x^207+4x^210+4x^213+8x^216+14x^219+6x^222+4x^225+4x^228+2x^234
The gray image is a linear code over GF(3) with n=279, k=8 and d=172.
This code was found by Heurico 1.16 in 96.9 seconds.