The generator matrix

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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+130x^141+162x^142+474x^143+1162x^144+1542x^145+2490x^146+2366x^147+3180x^148+4356x^149+4392x^150+4962x^151+6612x^152+5330x^153+6024x^154+5736x^155+3442x^156+2484x^157+1782x^158+956x^159+438x^160+300x^161+216x^162+78x^163+72x^164+114x^165+60x^166+18x^167+66x^168+18x^169+30x^170+32x^171+6x^172+18x^174

The gray image is a linear code over GF(3) with n=684, k=10 and d=423.
This code was found by Heurico 1.16 in 11.2 seconds.