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

generates a code of length 75 over Z3[X]/(X^3) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+54x^136+140x^138+462x^139+216x^140+642x^141+1614x^142+738x^143+1734x^144+3528x^145+2196x^146+3920x^147+5394x^148+3978x^149+6342x^150+7644x^151+3636x^152+4790x^153+5094x^154+2016x^155+1754x^156+1902x^157+342x^158+168x^159+462x^160+70x^162+72x^163+58x^165+18x^166+12x^168+12x^171+4x^174+18x^177+4x^180+10x^183+4x^189

The gray image is a linear code over GF(3) with n=675, k=10 and d=408.
This code was found by Heurico 1.16 in 11.9 seconds.