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 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 0 2X 0 X 0 X 0 2X 2X 0 X X X X 2X 0 X 2X 0 0 2X 2X 0 2X 2X 2X 2X 0 2X 2X X 2X 0 2X 2X 2X 0 X 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 0 X 0 X 2X 0 X 2X X 2X X X 0
0 0 X 0 0 0 X X X 2X 0 X 2X 0 2X 2X X X X 0 0 X X 0 0 2X X X 2X 2X 0 X 2X 2X 2X 2X 0 0 2X 2X X 2X 0 2X X 2X 0 X 0 X X 0 2X X 0 2X 0 2X X X 2X 0 2X 0 X X 0 2X 0 0 X X 2X 2X 2X 2X X 0 0 X 2X 0 0 0 X 2X X X 0 0 2X 0 X 2X 2X 0 X
0 0 0 X 0 X 2X X X 0 0 2X 2X X 0 0 X X 2X X 2X X 2X 0 X 2X 2X X 2X 0 0 2X 0 2X 2X 0 X 0 2X 2X 2X 0 0 2X 2X 0 X X X X X X 2X 2X 0 0 2X X 0 0 X 2X X 2X 0 0 2X X 2X 2X 0 0 X X X X 0 2X 2X 0 X 0 0 X 2X 2X X 0 0 X 2X X 0 X X 0 0
0 0 0 0 X 2X X 0 X X X 2X 0 2X X 0 2X X 0 X 2X 2X 2X 2X X X 0 0 0 2X X X 2X 2X 2X 0 0 0 0 2X 0 X 2X X X 0 X 2X 0 X 0 2X X 2X 2X 2X 0 0 X 2X 2X X X X X 0 2X X 0 0 X 0 2X X 0 0 2X X 2X 2X 2X 0 X 2X 2X 2X 2X 2X 0 X 0 0 X 2X 0 0 0
generates a code of length 97 over Z3[X]/(X^2) who´s minimum homogenous weight is 189.
Homogenous weight enumerator: w(x)=1x^0+116x^189+162x^192+324x^195+114x^198+10x^207+2x^288
The gray image is a linear code over GF(3) with n=291, k=6 and d=189.
This code was found by Heurico 1.16 in 0.207 seconds.