The generator matrix

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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+136x^141+60x^142+132x^143+422x^144+606x^145+1170x^146+1192x^147+1638x^148+2592x^149+2718x^150+4044x^151+6006x^152+4348x^153+5682x^154+7458x^155+4898x^156+4788x^157+4650x^158+2270x^159+1884x^160+1206x^161+446x^162+192x^163+66x^164+182x^165+54x^166+48x^167+70x^168+6x^169+14x^171+18x^174+20x^177+12x^180+8x^183+6x^186+4x^189+2x^192

The gray image is a linear code over GF(3) with n=693, k=10 and d=423.
This code was found by Heurico 1.16 in 14.2 seconds.