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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+54x^129+152x^132+216x^135+24x^137+218x^138+180x^140+206x^141+576x^143+194x^144+1086x^146+172x^147+13122x^148+1332x^149+160x^150+936x^152+158x^153+240x^155+146x^156+130x^159+116x^162+86x^165+84x^168+40x^171+22x^174+22x^177+4x^180+2x^183+2x^186+2x^201

The gray image is a linear code over GF(3) with n=666, k=9 and d=387.
This code was found by Heurico 1.16 in 3.99 seconds.