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 X X X X 0 X X X 0 X 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 X X 0 0 0 X 0 X X X X X X 2X X 2X 0
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 0 2X 2X 2X X 0 2X 2X X 0 2X 0 2X X 0 2X
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 0 0 0 X X 0 2X 0 2X 0 X 2X 0 X 2X 2X
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 0 X X 2X 2X X X 2X 2X 2X X X 0 2X 2X 2X 0
generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 103.
Homogenous weight enumerator: w(x)=1x^0+216x^103+144x^105+76x^108+270x^112+18x^132+4x^135
The gray image is a linear code over GF(3) with n=162, k=6 and d=103.
This code was found by Heurico 1.16 in 1.65 seconds.