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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+68x^138+78x^140+294x^141+24x^142+180x^143+478x^144+120x^145+492x^146+516x^147+732x^148+2166x^149+462x^150+2304x^151+4086x^152+484x^153+2364x^154+2760x^155+436x^156+240x^157+204x^158+420x^159+48x^160+162x^161+248x^162+42x^164+128x^165+36x^167+38x^168+32x^171+14x^174+6x^177+8x^180+4x^183+2x^186+4x^192+2x^204

The gray image is a linear code over GF(3) with n=684, k=9 and d=414.
This code was found by Heurico 1.16 in 2.88 seconds.