The generator matrix

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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 143.

Homogenous weight enumerator: w(x)=1x^0+384x^143+706x^144+1452x^145+3174x^146+3424x^147+3126x^148+5454x^149+4520x^150+4236x^151+6480x^152+4706x^153+4104x^154+5220x^155+3688x^156+2310x^157+3096x^158+1426x^159+684x^160+456x^161+206x^162+78x^163+12x^164+28x^165+24x^166+18x^167+6x^168+12x^169+6x^170+12x^175

The gray image is a linear code over GF(3) with n=684, k=10 and d=429.
This code was found by Heurico 1.16 in 9.36 seconds.