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 0 1 1 0 1 1 1 1 1 2X 1 1 1 1 1 0 1 0 1 X 2X 1 1 1 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 X 1 1 1 2X 1 1 1 X 1 1 1 2X 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 X 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 2X+1 2 X 2 0 1 2X+1 1 1 2 0 X+2 2X+1 0 1 2X+2 X 2X+1 2X+2 X 1 X 1 2X+1 1 1 X 2X+1 2 X 1 2X+2 X 0 2X+2 2X+1 1 2 2X 1 2X+1 0 X X+2 1 2X+2 X+1 2 1 1 X+1 2X 1 1 2X+1 2 1 1 X+1 2 X+2 1 0 2 0 2X+2 X+2 2 2X+1 X 2 2X+1 2X 2X+2 X+1 1 2X+1 X+2 0 0
0 0 2X 0 0 0 0 0 0 2X X 0 X X 2X X X X X 2X 0 X 0 X 0 0 2X 2X X 0 0 X X X 0 X 2X 2X 2X X X 0 0 2X X 2X X X X 2X 0 2X X 2X 2X 2X X X 0 0 2X 0 2X X X X 0 2X 2X 2X 0 X X X X X 2X 0 0 0 0 X 2X 2X X X X 2X 2X 0 0 X 0 0 X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X 2X 2X X X 0 X X 2X 0 2X 2X X 2X 2X 2X 0 X 0 X 0 2X 0 X 2X 2X 2X X X 0 0 0 X 2X 2X X 0 2X 0 0 2X 0 2X X 0 2X 0 2X 2X X X X X X X 0 X X X 2X 2X 2X 0 0 X 2X 0 2X 0 0 2X 2X 2X 0 2X 2X 0 2X X X 0 2X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 2X X 2X X X X 2X X 2X 2X X 2X 2X 2X 2X X 2X X 0 2X X 0 0 0 X X X X X X 2X X 0 2X 2X 2X 2X 2X 0 0 X 0 0 0 0 2X 0 X X 0 X X 2X X 0 X 0 2X X 2X 2X 2X 0 0 0 2X 2X 0 X X 2X X X X 0 0
0 0 0 0 0 2X 0 0 0 0 0 2X 0 X 0 0 2X X 2X 0 2X 0 2X 2X X X 0 0 2X X X X X X 2X X 2X 0 0 2X 0 2X 2X 2X 2X X 2X 2X 0 X X 2X 0 X X 0 X X 2X 2X 2X 2X X X 0 X X 0 0 0 0 0 X X X X X X X 2X X 0 X 2X 2X 2X 0 2X 2X 0 2X 0 X 0 2X 0 0
0 0 0 0 0 0 X 0 2X 2X X 0 0 2X 2X 2X 2X 0 2X X X 2X X X 2X 0 0 2X X X X 0 X X X X 0 0 X 0 2X 0 2X 2X 0 X 2X 0 0 0 2X 2X X 0 2X 0 0 X 0 0 0 0 2X X 2X 2X X 0 2X 0 X X 2X X X 2X 2X X X 0 X X X 2X 0 X 0 0 0 X X 0 2X 2X 2X X 0
0 0 0 0 0 0 0 X X 2X 0 X 2X X X X 0 X X 0 2X X 0 2X 0 X 0 0 X 2X X 2X X 0 X X X 0 X X 2X 0 2X X 2X X 2X 0 2X 2X X X X X X 0 0 2X X 2X 0 0 0 0 2X X X 2X X 2X 0 X X X 0 0 2X 0 2X 2X 2X X 2X X X 2X X 2X 2X 2X 0 0 0 X 0 0 0
generates a code of length 97 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.
Homogenous weight enumerator: w(x)=1x^0+78x^168+212x^171+514x^174+1068x^177+2088x^180+3042x^183+4932x^186+7046x^189+8512x^192+8718x^195+8626x^198+6492x^201+3840x^204+1980x^207+938x^210+428x^213+202x^216+126x^219+88x^222+64x^225+30x^228+16x^231+4x^234+2x^237+2x^240
The gray image is a linear code over GF(3) with n=291, k=10 and d=168.
This code was found by Heurico 1.16 in 94.9 seconds.