The generator matrix

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

generates a code of length 76 over Z3[X]/(X^2) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+216x^145+294x^146+70x^147+204x^148+210x^149+76x^150+198x^151+156x^152+18x^153+126x^154+90x^155+30x^156+66x^157+90x^158+26x^159+48x^160+48x^161+6x^162+48x^163+48x^164+8x^165+36x^166+24x^167+4x^168+24x^169+12x^170+6x^172+2x^177+2x^180

The gray image is a linear code over GF(3) with n=228, k=7 and d=145.
This code was found by Heurico 1.16 in 47.4 seconds.