The generator matrix

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

generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+126x^137+304x^138+408x^139+948x^140+1058x^141+900x^142+1620x^143+1678x^144+1182x^145+2172x^146+2234x^147+1554x^148+2070x^149+1382x^150+714x^151+756x^152+258x^153+60x^154+42x^155+86x^156+36x^157+24x^158+18x^159+6x^160+18x^161+14x^162+4x^165+4x^168+2x^171+4x^177

The gray image is a linear code over GF(3) with n=657, k=9 and d=411.
This code was found by Heurico 1.16 in 1.6 seconds.