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

generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+102x^150+168x^153+224x^156+18x^158+224x^159+180x^161+232x^162+720x^164+194x^165+1440x^167+13324x^168+1440x^170+126x^171+576x^173+126x^174+110x^177+102x^180+102x^183+72x^186+88x^189+44x^192+40x^195+12x^198+10x^201+6x^204+2x^237

The gray image is a linear code over GF(3) with n=756, k=9 and d=450.
This code was found by Heurico 1.16 in 4.67 seconds.