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.