The generator matrix

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

generates a code of length 75 over Z3[X]/(X^3) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+234x^139+324x^140+290x^141+1560x^142+1296x^143+1416x^144+4320x^145+2568x^146+2442x^147+7896x^148+3498x^149+3678x^150+9444x^151+4092x^152+3266x^153+6378x^154+2136x^155+1092x^156+1872x^157+300x^158+160x^159+240x^160+198x^161+22x^162+78x^163+84x^164+8x^165+24x^166+72x^167+8x^168+24x^169+12x^170+2x^171+6x^172+2x^174+4x^177+2x^183

The gray image is a linear code over GF(3) with n=675, k=10 and d=417.
This code was found by Heurico 1.16 in 14.5 seconds.