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

generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+74x^150+168x^151+126x^152+210x^153+228x^154+156x^155+126x^156+198x^157+66x^158+114x^159+150x^160+42x^161+50x^162+84x^163+30x^164+54x^165+84x^166+18x^167+46x^168+18x^169+12x^170+18x^171+12x^172+24x^173+18x^174+24x^175+6x^176+16x^177+6x^178+6x^182+2x^195

The gray image is a linear code over GF(3) with n=237, k=7 and d=150.
This code was found by Heurico 1.13 in 0.126 seconds.