The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  X  1  1  1  1  1  X  1  1  X  X  X  1  1  1  1  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 2X^2  0  0 2X^2 X^2 X^2 2X^2  0 2X^2 X^2  0 X^2 X^2 2X^2  0  0  0 2X^2 X^2  0 2X^2 X^2  0  0  0 X^2 X^2 2X^2 X^2  0 X^2  0 2X^2 2X^2 2X^2  0 X^2 X^2  0 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2  0 2X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2  0 X^2  0 X^2 X^2 2X^2 2X^2  0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 X^2 2X^2  0 2X^2  0 X^2 X^2  0 2X^2  0 X^2  0 X^2  0 X^2 X^2 2X^2  0  0 X^2 2X^2 X^2 X^2  0  0  0 2X^2  0  0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 X^2 2X^2 2X^2 X^2  0  0 2X^2  0 X^2  0  0 2X^2 X^2  0 2X^2  0  0 2X^2  0
 0  0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 X^2  0 X^2 2X^2 X^2 2X^2 2X^2 2X^2  0 X^2 X^2  0 2X^2 X^2  0  0  0 X^2 X^2 X^2 2X^2 2X^2 2X^2  0 X^2  0 2X^2  0 2X^2  0 2X^2 X^2  0 X^2  0 X^2 X^2 2X^2 2X^2  0  0 X^2  0  0 X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2  0 2X^2  0 X^2 X^2 X^2 X^2  0  0 2X^2  0 X^2 X^2  0 2X^2 2X^2  0 2X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2 X^2 2X^2 X^2  0  0
 0  0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2  0 2X^2 2X^2 X^2  0  0  0 X^2  0  0 2X^2 X^2 X^2 X^2  0  0 2X^2  0 2X^2 2X^2  0 2X^2 2X^2 X^2 X^2 2X^2 X^2  0 X^2 2X^2 X^2  0 2X^2 2X^2 X^2 X^2 X^2  0 2X^2  0  0  0  0 2X^2 X^2  0 2X^2  0 2X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 2X^2 X^2 X^2 2X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 2X^2  0
 0  0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 X^2  0  0 2X^2  0 2X^2 X^2 X^2 2X^2 2X^2 X^2  0  0 2X^2 2X^2 2X^2 2X^2  0  0 2X^2 X^2  0  0 2X^2 2X^2 X^2 2X^2  0 X^2 X^2 2X^2 X^2  0  0 2X^2 2X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 2X^2  0  0  0  0 X^2 2X^2  0  0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2  0  0  0  0  0 X^2 2X^2 2X^2  0  0 2X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2  0  0 X^2  0 2X^2 X^2 X^2 X^2 X^2 2X^2  0  0 X^2 2X^2  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2  0 2X^2 X^2  0 X^2  0  0 X^2 2X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 2X^2 2X^2  0 2X^2 2X^2  0 2X^2  0  0 2X^2 X^2 2X^2 X^2  0  0 X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 2X^2 X^2 X^2  0 2X^2 2X^2 X^2 X^2  0  0 X^2 2X^2

generates a code of length 94 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+38x^168+144x^171+218x^174+244x^177+382x^180+760x^183+1274x^186+13122x^188+1500x^189+1112x^192+332x^195+108x^198+88x^201+100x^204+76x^207+70x^210+44x^213+20x^216+18x^219+18x^222+6x^225+2x^228+2x^231+2x^234+2x^261

The gray image is a linear code over GF(3) with n=846, k=9 and d=504.
This code was found by Heurico 1.16 in 5.4 seconds.