The generator matrix

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

generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+234x^148+236x^150+306x^151+170x^153+258x^154+162x^157+168x^159+180x^160+66x^162+150x^163+90x^166+74x^168+54x^169+4x^171+24x^172+6x^177+2x^180+2x^186

The gray image is a linear code over GF(3) with n=234, k=7 and d=148.
This code was found by Heurico 1.16 in 79 seconds.