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 X X X X X X X 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 X X X 0 2X 2X 2X X X X 0 0 0 X X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 0
0 0 X 2X 2X X 0 X 2X 0 X 2X X 2X 0 0 X 2X 0 X 2X X 2X 0 0 X 2X 0 X 2X X 2X 0 0 X 2X 0 X 2X X 2X 0 0 X 2X X 2X X 0 2X 0 X 2X 0 X 2X X 0 X 2X X 2X 0 0 X 2X 0 X 2X X 2X 0 0 X 0
generates a code of length 75 over Z3[X]/(X^2) who´s minimum homogenous weight is 150.
Homogenous weight enumerator: w(x)=1x^0+60x^150+12x^153+6x^156+2x^189
The gray image is a linear code over GF(3) with n=225, k=4 and d=150.
This code was found by Heurico 1.16 in 0.0457 seconds.