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

generates a code of length 97 over Z3[X]/(X^3) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+66x^174+136x^177+230x^180+6x^181+198x^183+84x^184+210x^186+306x^187+194x^189+726x^190+154x^192+1218x^193+13122x^194+144x^195+1152x^196+120x^198+726x^199+142x^201+156x^202+140x^204+104x^207+84x^210+82x^213+62x^216+46x^219+36x^222+16x^225+10x^228+6x^231+2x^237+2x^243+2x^267

The gray image is a linear code over GF(3) with n=873, k=9 and d=522.
This code was found by Heurico 1.16 in 5.61 seconds.