The generator matrix

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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 133.

Homogenous weight enumerator: w(x)=1x^0+120x^133+390x^134+378x^135+918x^136+1908x^137+1794x^138+2484x^139+3858x^140+4494x^141+4044x^142+5286x^143+5904x^144+5340x^145+6180x^146+5302x^147+3348x^148+3276x^149+1618x^150+894x^151+672x^152+110x^153+210x^154+162x^155+48x^156+54x^157+102x^158+18x^159+72x^160+24x^161+6x^162+12x^163+12x^164+2x^165+8x^168

The gray image is a linear code over GF(3) with n=648, k=10 and d=399.
This code was found by Heurico 1.16 in 11.5 seconds.