The generator matrix

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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+328x^135+378x^136+1866x^137+2898x^138+2466x^139+4242x^140+5204x^141+3882x^142+5190x^143+6580x^144+4638x^145+5268x^146+5018x^147+2736x^148+3390x^149+2316x^150+768x^151+906x^152+624x^153+150x^154+12x^155+80x^156+36x^157+18x^158+28x^159+12x^160+6x^161+6x^162+2x^165

The gray image is a linear code over GF(3) with n=648, k=10 and d=405.
This code was found by Heurico 1.16 in 8.35 seconds.