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

generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+30x^154+96x^155+90x^156+162x^157+228x^158+120x^159+420x^160+438x^161+106x^162+852x^163+1656x^164+100x^165+1788x^166+3912x^167+64x^168+2076x^169+3870x^170+42x^171+1248x^172+1068x^173+52x^174+402x^175+210x^176+38x^177+204x^178+114x^179+26x^180+84x^181+42x^182+8x^183+24x^184+24x^185+28x^186+6x^188+8x^189+10x^192+18x^195+4x^198+6x^201+2x^204+2x^207+2x^210+2x^219

The gray image is a linear code over GF(3) with n=756, k=9 and d=462.
This code was found by Heurico 1.16 in 93.6 seconds.