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 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
0 X 0 0 0 0 0 0 0 0 2X X X X X X X X X X 2X 0 0 X X 2X X 0 0 0 X 0 2X X 2X X 2X X 2X 0 2X X 0 2X X 0 2X 0 2X 2X 2X 2X 2X 2X 2X 0 X 2X 2X 2X 0 0 X X 2X 2X 0 0 X X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 0 0 X X 0 2X 2X X
0 0 X 0 0 0 X X X 2X 0 X 2X X X 2X 2X 0 X X 0 X 0 2X 0 X 0 X 0 0 X X 0 0 X 0 X 0 X X 0 X 0 X 0 2X 2X 2X X 0 0 2X X 0 2X 2X X X 2X 0 0 X X 0 0 X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 X 2X X X 0 X X
0 0 0 X 0 X 2X 2X X 2X 0 0 2X 2X 0 0 X X X 2X X X X 2X 0 2X X 0 2X 2X 2X 2X 0 0 X 2X 0 2X 0 0 2X X 2X X X 0 X X 0 X 0 X 2X 2X 2X X 0 2X 2X 2X 0 X X 2X X X 0 2X X 0 0 0 0 X 2X X 2X 0 0 X 2X 0 0 X 2X 2X X 0 0 0 2X
0 0 0 0 X 2X 2X 0 2X 2X X X 2X X 0 X X 2X 2X 2X 2X X X 0 2X 0 X 2X 0 2X 0 X 0 X X 2X X 0 0 X 2X X X 2X 0 X X 2X 2X X 2X 2X 2X X 0 X 2X X 2X 0 2X 0 0 X 0 0 0 0 2X 0 0 X 2X 0 X 0 X 2X 2X 0 X 0 X 2X 2X 2X X 2X X X 2X
generates a code of length 91 over Z3[X]/(X^2) who´s minimum homogenous weight is 177.
Homogenous weight enumerator: w(x)=1x^0+72x^177+222x^180+324x^183+90x^186+18x^189+2x^270
The gray image is a linear code over GF(3) with n=273, k=6 and d=177.
This code was found by Heurico 1.16 in 0.122 seconds.