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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+158x^141+132x^142+234x^143+574x^144+270x^145+534x^146+628x^147+888x^148+1572x^149+566x^150+1980x^151+5436x^152+496x^153+1908x^154+1866x^155+370x^156+372x^157+348x^158+344x^159+144x^160+108x^161+252x^162+48x^163+84x^164+142x^165+54x^166+24x^167+84x^168+30x^169+18x^171+6x^172+10x^174+2x^201

The gray image is a linear code over GF(3) with n=684, k=9 and d=423.
This code was found by Heurico 1.16 in 2.56 seconds.