The generator matrix

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

generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+516x^144+1248x^147+2206x^150+2738x^153+2858x^156+2994x^159+2426x^162+2242x^165+1326x^168+764x^171+244x^174+68x^177+20x^180+8x^183+12x^186+4x^189+6x^192+2x^198

The gray image is a linear code over GF(3) with n=237, k=9 and d=144.
This code was found by Heurico 1.16 in 12.9 seconds.