The generator matrix

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

generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+82x^96+54x^99+162x^100+324x^103+60x^105+14x^108+18x^114+12x^117+2x^150

The gray image is a linear code over GF(3) with n=153, k=6 and d=96.
This code was found by Heurico 1.16 in 0.0951 seconds.