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 X X 1 1 1 X 1 1 X 1 1 1 X 1 1 X X X 1 0 1
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 X 0 0 X X X 2X 0 X 2X 0 X 2X 2X 2X 0 X 0 X X 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 0 2X X 2X 2X 0 0 0 X 2X 0 2X 0 2X 2X 2X X X X 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 X 0 0 0 X 2X 2X 0 X 2X 0 X X 0 0 0 X X X X
generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 111.
Homogenous weight enumerator: w(x)=1x^0+132x^111+28x^114+18x^117+60x^120+2x^132+2x^144
The gray image is a linear code over GF(3) with n=171, k=5 and d=111.
This code was found by Heurico 1.16 in 2.14 seconds.