The generator matrix

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

generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+78x^78+192x^79+146x^81+324x^82+148x^84+246x^85+112x^87+306x^88+140x^90+288x^91+58x^93+96x^94+22x^96+6x^97+8x^99+4x^102+4x^105+2x^108+6x^111

The gray image is a linear code over GF(3) with n=129, k=7 and d=78.
This code was found by Heurico 1.16 in 0.0813 seconds.