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

generates a code of length 74 over Z3[X]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+102x^146+30x^147+54x^149+36x^150+6x^153+6x^156+2x^162+6x^173

The gray image is a linear code over GF(3) with n=222, k=5 and d=146.
This code was found by Heurico 1.16 in 11.1 seconds.