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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+30x^148+292x^150+108x^151+60x^152+376x^153+276x^154+120x^155+640x^156+1002x^157+276x^158+1400x^159+2832x^160+300x^161+2496x^162+3720x^163+342x^164+1818x^165+1902x^166+264x^167+450x^168+168x^169+72x^170+300x^171+102x^172+24x^173+110x^174+36x^175+52x^177+24x^178+28x^180+6x^181+10x^183+14x^186+6x^189+10x^192+4x^195+4x^198+2x^201+2x^204+2x^207+2x^210

The gray image is a linear code over GF(3) with n=729, k=9 and d=444.
This code was found by Heurico 1.16 in 35.7 seconds.