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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+82x^150+114x^151+216x^152+484x^153+204x^154+306x^155+964x^156+510x^157+498x^158+1580x^159+498x^160+318x^161+342x^162+54x^163+24x^164+48x^165+24x^166+24x^167+66x^168+36x^169+60x^170+50x^171+12x^172+12x^173+18x^174+6x^175+6x^177+2x^183+2x^216

The gray image is a linear code over GF(3) with n=711, k=8 and d=450.
This code was found by Heurico 1.16 in 0.524 seconds.